Patent Publication Number: US-2023135412-A1

Title: System and method for damping machine-induced vibrations in a workpiece

Description:
PRIORITY 
     This application claims priority from U.S. Ser. No. 63/275,048 filed on Nov. 3, 2021. 
    
    
     FIELD 
     The present disclosure relates generally to workpiece processing and, more particularly, to systems and methods for damping machine-induced vibrations in a workpiece induced during a machining operation. 
     BACKGROUND 
     Composite parts are commonly used in applications where light weight and high strength are desired, such as in aircraft and vehicles. Typically, one or more machining or other processing operations are performed on the composite part, such as drilling holes, machining features, and trimming edges. However, composite parts may tend to vibrate during the machining operation. Such vibrations may present challenges related to the accuracy of the machining operation. As such, post-machining operations, such as shimming or rework, may be required. These challenges may also limit the capacity for determinant assembly or predictive assembly of a manufactured structure that includes the composite part. Accordingly, those skilled in the art continue with research and development efforts in the field of composite manufacturing. 
     SUMMARY 
     Disclosed are examples of a system for damping vibrations in a workpiece, a damping apparatus for controlling machine-induced vibrations in a workpiece, a method for damping vibrations in a workpiece, a method for selectively increasing a mass of a workpiece, a method for modifying a natural frequency of a workpiece, and a workpiece manufactured using the system or the damping apparatus and according to the methods. The following is a non-exhaustive list of examples, which may or may not be claimed, of the subject matter according to the present disclosure. 
     In a first example, the disclosed system includes a plurality of workpiece holders to hold a workpiece in a work cell. The system also includes a machine tool located in the work cell. The machine tool performs a machining operation on the workpiece while the workpiece is held by the plurality of workpiece holders. The system further includes a damping apparatus coupled to the workpiece. The damping apparatus controls machine-induced vibrations in the workpiece during the machining operation. 
     In a second example, the disclosed method is performed using the system of the first example. 
     In a third example, the disclosed workpiece is manufactured using the system of the first example. 
     In a fourth example, the disclosed method if for fabricating a portion of an aircraft using the system of the first example. 
     In a fifth example, the disclosed damping apparatus includes a fixture base and a plurality of grippers coupled to the fixture base. Each one of the plurality of grippers is selectively extendable and retractable relative to the fixture base to be selectively connected to the workpiece. 
     In a sixth example, the disclosed system includes the damping apparatus of the fifth example. 
     In a seventh example, the disclosed method is performed using the damping apparatus of the fifth example. 
     In an eighth example, the disclosed method is for fabricating a portion of an aircraft using the damping apparatus of the fifth example. 
     In a ninth example, the disclosed workpiece is manufactured using the damping apparatus of the first example. 
     In a tenth example, the disclosed method includes steps of: (1) holding a workpiece; (2) selectively controlling a natural frequency of the workpiece; and (3) performing a machining operation on the workpiece. 
     In an eleventh example, the disclosed system is implemented according to the method of the tenth example. 
     In a thirteenth example, the disclosed workpiece is manufactured according to the method of the tenth example. 
     In a fourteenth example, a portion of an aircraft is assembled according to the method of the tenth example. 
     In a fifteenth example, the disclosed method includes steps of: (1) selecting one or more locations on a workpiece; and (2) coupling a damping apparatus the workpiece at the one or more locations; and (3) increasing a mass of a portion of the workpiece, including the one or more locations, by a mass of the damping apparatus. 
     In a sixteenth example, the disclosed method includes steps of: (1) determining a natural frequency of a workpiece; and (2) modifying a natural frequency of at least a portion of the workpiece by increasing a mass or a stiffness of at least a portion of the workpiece when an oscillating force is applied to the workpiece by a machine tool during a machining operation. 
     Other examples of the disclosed system, damping apparatus, method, and workpiece will become apparent from the following detailed description, the accompanying drawings, and the appended claims. 
    
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
         FIG.  1    is a schematic illustration of an example of a manufacturing environment for processing of a workpiece; 
         FIG.  2    is a schematic block diagram of an example of a system for damping machine-induced vibrations; 
         FIG.  3    is a schematic, perspective view of an example of a portion of the system, depicting a plurality of workpiece holders, a workpiece held by the plurality of workpiece holders, and a plurality of damping apparatuses; 
         FIG.  4    is a schematic, perspective view of an example of a portion of the system, depicting the plurality of workpiece holders, an overhead workpiece handler, the workpiece held by the plurality of workpiece holders and the overhead workpiece handler, the plurality of damping apparatuses, and a metrology system; 
         FIG.  5    is a schematic, perspective view of an example of a portion of the system, depicting the plurality of workpiece holders, the overhead workpiece handler, the workpiece held by the plurality of workpiece holders and the overhead workpiece handler, and the plurality of damping apparatuses; 
         FIG.  6    is a schematic illustration of an example of a portion of the system, depicting the plurality of workpiece holders, the overhead workpiece handler, the workpiece held by the plurality of workpiece holders and the overhead workpiece handler, one of the plurality of damping apparatuses, the metrology system, and a plurality of machine tools; 
         FIG.  7    is a schematic, perspective view of an example of one of the damping apparatuses; 
         FIG.  8    is a schematic illustration of an example of a portion of one of the damping apparatuses, depicting a selection of a plurality of grippers connected to the workpiece at a plurality of selected locations; 
         FIG.  9    is a schematic illustration of an example of one of the plurality of grippers, depicted in a first position; 
         FIG.  10    is a schematic illustration of an example of one of the plurality of grippers, depicted in a second position; 
         FIG.  11    is a schematic illustration of an example of one of the plurality of grippers, depicted in a third position; 
         FIG.  12    is a schematic, sectional view of an example of one of the plurality of grippers; 
         FIG.  13    is a flow diagram of an example of a method for damping vibrations in a workpiece; 
         FIG.  14    is a flow diagram of an example of a method for increasing a mass of a workpiece; 
         FIG.  15    is a flow diagram of an example of a method for modifying a natural frequency of a workpiece; 
         FIG.  16    is a flow diagram of an example of an aircraft manufacturing and service method; and 
         FIG.  17    is a schematic illustration of an example of an aircraft. 
     
    
    
     DETAILED DESCRIPTION 
     Referring generally to  FIGS.  1 - 12   , by way of examples, the present disclosure is directed to a system  100  for damping vibrations in a workpiece  102 . The system  100  facilitates one or more processing operation, such as at least one machining operation, being performed on the workpiece  102 . Additionally, the system  100  facilitates automated indexing of the workpiece  102  within a work cell and conformance of the workpiece  102  to a predetermined or desired shape within the work cell during a processing operation. As such, the system  100  advantageously improves the accuracy and precision of the machining operation and facilitates determinant assembly or predictive assembly of a structure that includes the workpiece  102 . 
     In one or more examples, the workpiece  102  is made of a composite material, such as a fiber reinforced polymer (e.g., a composite workpiece). In one or more examples, the workpiece  102  is made of a metallic material (e.g., a metallic workpiece). In still other examples, the workpiece  102  is made of any other suitable material or combination of materials. 
     For the purpose of the present disclosure, the term “composite workpiece” (e.g., the workpiece  102 ) refers to any object, article, item, or structure made of a cured composite material. For the purpose of the present disclosure, the term “post-cure” refers to a condition of a composite material after a curing operation, such as by application of heat and/or pressure, to cure, anneal, dry, and/or harden the composite material. 
     In one or more examples, the workpiece  102  is, or forms, a part of or a component of a larger manufactured article or structure, such as an aircraft (e.g., aircraft  1200  shown in  FIG.  15   ) or a component of an aircraft. As an example, the workpiece  102  is a wing panel  1230  (e.g., as shown in  FIG.  15   ) of the aircraft  1200 . 
     It can be appreciated that a machining operation (e.g., drilling, boring, milling, cutting, routing, trimming, etc.) performed on a workpiece (e.g., a composite workpiece or a metallic workpiece) may tend to induce vibrations in the workpiece. Such vibrations may move the workpiece away from a desired, or indexed, position and/or may temporarily change the shape of the workpiece away from a desired shape during machining. Such movement and/or deformation may lead to inaccuracies in the machining operation. The undesirable effect of such vibrations may increase for relatively long and thin workpieces, such as panels, stiffeners, and the like. 
     It is therefore desirable to hold a workpiece in a fixed position during a machining operation to prevent vibration, or “chatter,” which can produce surface flaws in the workpiece. It is also desirable to prevent deflection of the workpiece under a machining load, which can reduce machining accuracy. Additionally, it is desirable to perform several machining operations in the same location, for example, in a manufacturing work cell, using the same machine tool for different workpieces. 
     The principles and implementations of the system  100  disclosed herein enable the workpiece  102  to be maintained at a desired position and/or maintained in a desired shape during a machining operation while damping machine-induced vibrations. As such, machining inaccuracies or inconsistencies due to vibrations may be reduced or eliminated. 
     Referring now to  FIG.  1   , in one or more examples, a manufacturing environment  224  facilitates processing of the workpiece  102 , such as machining (e.g., drilling, boring, milling, routing, etc.), trimming (e.g., cutting), coating, painting, sub-assembly (e.g., assembly of other parts of components to the workpiece  102 ), and the like. In reference to a composite workpiece, the processing refers to post-cure processing of the workpiece  102 . 
     Generally, the manufacturing environment  224  includes a plurality of work cells  226 , identified individually as a first work cell  228 , a second work cell  230 , a third work cell  232 , a fourth work cell  234 , a fifth work cell  236 , etc. The manufacturing environment  224  may include any number of work cells  226 , depending, for example, on a number of processing operations to be performed on the workpiece  102 . 
     Each one of the work cells  226  facilitates or corresponds to a different processing operation associated with the manufacture of the workpiece  102 . In one or more examples, each one of the work cells  226  includes one or more systems, sub-systems, apparatuses, and/or machines (not shown in  FIG.  1   ) that perform at least one processing operation. In one or more examples, the work cells  226  are interlinked (e.g., in series or in parallel) and cooperate to automate at least a portion of the fabrication process. 
     In one or more examples, the system  100  includes, or is associated with, at least one of the work cells  226 . In an example, at least a portion of the system  100  (e.g., one or more components of the system  100 ) is associated with the second work cell  230  (e.g., as shown in  FIGS.  3 - 7   ). In another example, at least a portion of the system  100  (e.g., one or more components of the system  100 ) is associated with another one of the work cells  226 . In one or more examples, the system  100  forms a sub-system of the manufacturing environment  224 . 
     In one or more examples, the system  100  facilitates transporting the workpiece  102  through the work cells  226 . In one or more examples, the system  100  also facilitates holding the workpiece  102  in each one of the work cells  226 . In one or more examples, the system  100  further facilitates performing at least one processing operation on the workpiece  102  in each one of the work cells  226 . In one or more examples, the system  100  additionally facilitates damping machine-induced vibrations in the workpiece  102  during the processing operation. 
     In one or more examples, the system  100  also facilitates indexing the workpiece  102  relative to each one of the work cells  226 . In one or more examples, the system  100  further facilitates conforming the workpiece  102  to a desired shape in each one of the work cells  226 . In one or more examples, the system  100  additionally facilitates generating and/or updating a digital model of the workpiece  102  after a processing operation is performed on the workpiece  102 . 
     Referring now to  FIG.  2   , in one or more examples, the system  100  includes a plurality of workpiece holders  106 . The workpiece holders  106  hold the workpiece  102  in one of the work cells  226  (e.g., the second work cell  230  as shown in  FIGS.  3 - 6   ). In one or more examples, more than one of the work cells  226  (e.g., the second work cell  230 , the third work cell  232 , the fourth work cell  234 , etc.) includes the workpiece holders  106 . 
     In one or more examples, the system  100  includes a machine tool  134 , which may also be referred to as a machining tool. The machine tool  134  is positioned in one of the work cells  226  (e.g., the second work cell  230  as shown in  FIGS.  4  and  6   ). The machine tool  134  performs at least one machining operation on the workpiece  102  while the workpiece  102  is held by the workpiece holders  106 . In one or more examples, more than one of the work cells  226  (e.g., the second work cell  230 , the third work cell  232 , the fourth work cell  234 , etc.) includes the machine tool  134 . 
     In one or more examples, the system  100  includes a damping apparatus  174 . The damping apparatus  174  is positioned in one of the work cells  226  (e.g., the second work cell  230  as shown in  FIGS.  3 - 7   ). The damping apparatus  174  is selectively coupled to the workpiece  102 . The damping apparatus  174  selectively controls machine-induced vibrations in the workpiece  102  during the machining operation. For example, the damping apparatus  174  reduces vibrations in the workpiece  102  that are induced by the machining operation. In one or more examples, more than one of the work cells  226  (e.g., the second work cell  230 , the third work cell  232 , the fourth work cell  234 , etc.) includes the damping apparatus  174 . 
     Throughout the present disclosure, vibrations in the workpiece  102  that are induced by the machining operation may also be referred to as machine-induced vibrations and refer to vibrations resulting from or induced by interaction between the machine tool  134  and the workpiece  102  during the machining operation. 
     In one or more examples, the system  100  includes a plurality of damping apparatuses  104 . At least one of the damping apparatuses  104  (e.g., the damping apparatus  174 ) is positioned between a directly adjacent pair of the workpiece holders  106  (e.g., as shown in  FIGS.  3 - 7   ). 
     Referring now to  FIGS.  3 - 7   , which illustrate examples of the second work cell  230 . It can be appreciated that the examples of the second work cell  230 , described herein and illustrated in  FIGS.  3 - 7   , may be substantially the same as any other one of the work cells  226  (e.g., the third work cell  232 , the fourth work cell  234 , etc.). For example, any one of the work cells  226  may include substantially the same features (e.g., workpiece holders  106 , machine tool  134 , damping apparatus  174 , etc.) and/or operate in substantially the same manner as the examples of the second work cell  230 , while performing the same or a different processing operation as another one of the work cells  226 . 
     Referring to  FIGS.  3 - 6   , in one or more examples, each one of the workpiece holders  106  is selectively controlled to index the workpiece  102  in the second work cell  230 . For example, with the workpiece  102  held by the workpiece holders  106 , the workpiece holders  106  appropriately position the workpiece  102  in the second work cell  230  for performance of a processing operation, for example, performed by the machine tool  134 . 
     Appropriately positioning and/or indexing the workpiece  102  in each one of the work cells  226  (e.g., the second work cell  230 ) using the workpiece holders  106  may be performed by any suitable manner or technique. As an example, the workpiece holders  106  utilizes repeatable machine positioning and machine accuracy to appropriately position and/or index the workpiece  102 . As another example, the system  100  utilizes a metrology system  108  (e.g., as shown in  FIGS.  2 ,  5  and  6   ) to provide appropriate positioning and/or indexing of the workpiece  102 . 
     Additionally, in one or more examples, the workpiece holders  106  conform the workpiece  102  to a desired shape of the workpiece  102 , for example, before and/or during performance of a processing operation. 
     In one or more examples, the desired shape of the workpiece  102  is an as-built shape of the workpiece  102 . For the purpose of the present disclosure, the term “as-built,” such as in reference to an as-built condition or an as-built shape of the workpiece  102 , refers to a condition of the workpiece  102  in which the workpiece  102  has a shape (e.g., geometry, profile, contour, structural features, and the like) that is substantially the same as a design or nominal shape of the workpiece  102 . In reference to a composite workpiece, the term “as-built,” such as in reference to an as-built condition or an as-built shape of the workpiece  102 , refers to a condition of the workpiece  102  in which the workpiece  102  has a shape (e.g., geometry, profile, contour, structural features, and the like) that is substantially the same as a shape of the workpiece  102  on a tool upon which the workpiece  102  was cured (e.g., tool  150  as shown in  FIG.  1   ). In other words, as an example, the desired or as-built shape of the workpiece  102  is a shape of the workpiece  102  that is substantially the same as a shape of the workpiece  102  as cured on a tool or mandrel (e.g., tool  150 ) and prior to separation from the tool or mandrel. 
     In one or more examples, the desired shape of the workpiece  102  is an as-machined shape of the workpiece  102 . For the purpose of the present disclosure, the term “as-machined,” such as in reference to an as-machined condition or an as-machined shape of the workpiece  102 , refers to a post-processing condition of the workpiece  102  in which the workpiece  102  has a shape (e.g., geometry, profile, contour, structural features, and the like) after a processing operation (e.g., one or more machining operations) is performed on the workpiece  102 . 
     In one or more examples, each one of the workpiece holders  106  (e.g., workpiece holder  244  shown in  FIG.  1   ) includes a base  128  and a clamp  120  that is coupled to the base  128 . The clamp  120  is configured to or is operable to clamp (e.g., hold and secure) the workpiece  102  is a predetermined position and prevent movement of the workpiece  102 . In one or more examples, the clamp  120  is a C-shaped clamp. 
     In one or more examples, the clamp  120  of each one of the workpiece holders  106  includes a first jaw  122 , a support member  124  that is coupled to the first jaw  122 , and a second jaw  126  that is coupled to the support member  124 . The second jaw  126  is movable (e.g., linearly movable) along the support member  124  relative to the first jaw  122  to clamp or unclamp the workpiece  102  between the first jaw  122  and the second jaw  126 . 
     In one or more examples, the workpiece  102  includes a first surface  144  and a second surface  220  that is opposite the first surface  144 . In one or more examples, the first jaw  122  contacts the first surface  144  and the second jaw  126  contacts the second surface  220  when the workpiece  102  is clamped by the clamp  120 . 
     Referring briefly to  FIGS.  3  and  4   , in one or more examples, with the workpiece  102  clamped between the first jaw  122  and the second jaw  126 , the second jaw  126  and the first jaw  122  conform the workpiece  102  to the desired shape. In one or more examples, the clamp  120  includes a plurality of numerical control contacts  136 . Throughout the present disclosure, the term “numerical control” may be referred to as “NC.” The numerical control contacts  136  are located along the first jaw  122 . The clamp  120  also includes a plurality of force control contacts  138 . The force control contacts  138  are located along the second jaw  126 . 
     Each one of the numerical control contacts  136  is selectively movable (e.g., extendable and retractable) relative to the first jaw  122  to a numerical control location. In one or more examples, the numerical control location for each one of the numerical control contacts  136  is predetermined or preprogrammed, for example, based on the desired shape of the workpiece  102 . For example, the numerical control locations correspond to coordinate locations on the first surface  144  of the workpiece  102  represented by an as-built model  116  of the workpiece  102 . As such, with each one of the numerical control contacts  136  at the numerical control location, the numerical control contacts  136  match a shape or contour of the first surface  144  of the workpiece  102  having the desired shape. 
     Each one of the force control contacts  138  is selectively movable (e.g., extendable and retractable) relative to the second jaw  126  to apply a shaping force to the workpiece  102 . The shaping force, applied by each one of the force control contacts  138 , forces the workpiece  102  against the numerical control contacts  136  to conform the workpiece  102  to the desired shape of the workpiece  102 . 
     In one or more examples, a portion of the first surface  144  of the workpiece  102  is supported on, is support by, or is in contact with one or more of the numerical control contacts  136  before the workpiece  102  is clamped between the first jaw  122  and the second jaw  126 . The second jaw  126  is moved toward the first jaw  122  to move the force control contacts  138  toward the second surface  220  of the workpiece  102 . In one or more examples, the second jaw  126  is moved toward the first jaw  122  until at least one of the force control contacts  138  is in contact with the second surface  220  of the workpiece  102 . In one or more examples, the second jaw  126  is moved toward the first jaw  122  to clamp a portion of the workpiece  102  between the first jaw  122  and the second jaw  126  and, more particularly, between at least one of the numerical control contacts  136  and at least one of the force control contacts  138 . With the workpiece  102  initially clamped between the first jaw  122  and the second jaw  126  and, more particularly, between at least one of the numerical control contacts  136  and at least one of the force control contacts  138 , each one of the force control contacts  138  moves into contact with the second surface  220  of the workpiece  102  and applies the shaping force to urge the portion of the workpiece  102  toward and against the numerical control contacts  136 . 
     In one or more examples, the clamp  120  is movable relative to the base  128 . For example, the clamp  120  is linearly movable along at least one axis and/or is rotationally moveable about at least one axis relative to the base  128 . With the workpiece  102  clamped by the clamp  120 , movement of the clamp  120  relative to the base  128  appropriately positions (e.g., indexes) the workpiece  102  in the second work cell  230 . With the workpiece  102  unclamped (e.g., released) from the clamp  120 , movement of the clamp  120  relative to the base  128  appropriately positions the clamp  120  in the second work cell  230  and/or relative to the workpiece  102 . 
     In one or more examples, the base  128  is movable relative to the second work cell  230 . For example, the base  128  is linearly movable along at least one axis and/or is rotationally moveable about at least one axis relative to the second work cell  230 . With the workpiece  102  clamped by the clamp  120 , movement of the base  128  appropriately positions (e.g., indexes) the workpiece  102  in the second work cell  230 . With the workpiece  102  unclamped from the clamp  120 , movement of the base  128  appropriately positions the clamp  120  in the second work cell  230  and/or relative to the workpiece  102 . 
     In one or more examples, with the workpiece  102  held by the clamp  120  of each one of the workpiece holders  106 , the clamp  120  rotates relative to the base  128  to adjust an angular orientation of the workpiece  102 . For example, the workpiece holders  106  rotate the workpiece  102  from a first orientation (e.g., approximately horizontal as shown in  FIG.  3   ) to a second orientation (e.g., approximately vertical as shown in  FIGS.  4  and  5   ) for performance of a processing operation. In the illustrated examples, the workpiece  102  is loaded onto the workpiece holders  106  in an approximately horizontal orientation (e.g., as shown in  FIG.  3   ) and is repositioned to an approximately vertical orientation (e.g., as shown in  FIGS.  4 - 6   ) for performance of a machining operation. However, in other examples, the workpiece  102  is loaded onto the workpiece holders  106  in an approximately vertical orientation and is repositioned to an approximately horizontal orientation for performance of a machining operation. In yet still other examples, the workpiece  102  is loaded onto the workpiece holders  106  in an approximately horizontal or vertical orientation and is maintained in that orientation for performance of a machining operation, while being selectively positioned for indexing. The orientation of the workpiece  102  when being loaded onto the workpiece holders  106  and/or while undergoing a machining operation may depend on various factors, such as, but not limited to, the configuration (e.g., geometry, size, shape, material composition, etc.) of the workpiece  102 , the type of machining operation performed on the workpiece  102 , the type of machine tool  134  performing the machining operation, and the like. 
     In one or more examples, the workpiece  102  is initially positioned or loaded in the clamp  120 , between the first jaw  122  and the second jaw  126 , in the first orientation (e.g., approximately horizontal orientation as shown in  FIG.  3   ). With the workpiece  102  in the first orientation (e.g., approximately horizontal orientation), the clamp  120  clamps the workpiece  102  between the first jaw  122  and the second jaw  126  and, more particularly, between the numerical control contacts  136  and the force control contacts  138 . In one or more examples, the numerical control contacts  136  and the force control contacts  138  conform the workpiece  102  to the desired shape. 
     As illustrated in  FIGS.  3 - 6   , in one or more examples, the clamp  120  rotationally moves relative to the base  128  to move the workpiece  102  from the first orientation (e.g., approximately horizontal orientation) to the second orientation (e.g., approximately vertical orientation as shown in  FIGS.  4  and  5   ). In one or more examples, a processing operation (e.g., drilling operation) is performed on the workpiece  102  in the second orientation (e.g., approximately vertical orientation as shown in  FIG.  5   ). Additionally, movement of the clamp  120  relative to the base  128  and/or movement of the base  128  relative to the second work cell  230  indexes the workpiece  102  for performance of the processing operation. 
     Referring now to  FIGS.  4  and  5   , in one or more examples, the damping apparatus  174  is selectively coupled to the workpiece  102  after the workpiece holders  106  position (e.g., index) the workpiece  102  in the second work cell  230  and/or after the workpiece holders  106  conform the workpiece  102  to the desired shape (e.g., when performed). In one or more examples, the damping apparatus  174  is selectively coupled to the first surface  144  of the workpiece  102 . 
     In the illustrated examples, the workpiece holders  106  position and hold the workpiece  102  in an upright or upstanding position such that the first surface  144  of the workpiece  102  is generally oriented in an approximately vertical position. In such examples, the damping apparatus  174  access, engages and is coupled to the workpiece  102  from the side. In other examples (not shown), the workpiece holders  106  position and hold the workpiece  102  in a side lying or prostrate position such that the first surface  144  of the workpiece  102  is in an approximately horizontal orientation. In such examples, the damping apparatus  174  access, engages and is coupled to the workpiece  102  from the top or the bottom. 
     In one or more examples, the damping apparatus  174  selectively controls a natural frequency  250  ( FIG.  2   ) of the workpiece  102 . In one or more examples, the damping apparatus  174  selectively modifies the natural frequency  250  ( FIG.  2   ) of the workpiece  102 . For example, with the damping apparatus  174  coupled to the workpiece  102 , the damping apparatus  174  selectively controls or modifies the natural frequency  250  of a portion of the workpiece  102 , for example, a portion  254  (e.g., as shown in  FIGS.  4  and  5   ) of the workpiece  102  that extends between the directly adjacent pair of the workpiece holders  106 . 
     The natural frequency  250  of the workpiece  102 , or any portion of the workpiece  102  (e.g., portion  254 ), is the frequency at which the workpiece  102  resonates or tends to oscillate. 
     In one or more examples, the natural frequency  250  of the workpiece  102 , or of a portion (e.g., the portion  254 ) of the workpiece  102 , is selectively controlled or otherwise modified by increasing a mass  103  (e.g., as shown in  FIG.  2   ) of the portion  254  of the workpiece  102  using the damping apparatus  174 . For example, with the damping apparatus  174  coupled to the portion  254  of the workpiece  102 , the mass  103  of the portion  254  is increased by a mass  107  (e.g., as shown in  FIG.  2   ) of the damping apparatus  174 . 
     In one or more examples, the natural frequency  250  of the workpiece  102 , or of a portion of the workpiece  102 , is modified by increasing a stiffness  105  of a portion of the workpiece  102 . For example, with the damping apparatus  174  coupled to the portion  254  of the workpiece  102 , the stiffness  105  of the portion  254  is increased by connection of the damping apparatus  174 . 
     In one or more examples, the natural frequency  250  of the portion  254  of the workpiece  102  is selectively controlled or modified such that the natural frequency  250  of the portion  254  of the workpiece  102  is different than a frequency  260  of an oscillating force  256  ( FIG.  2   ) applied to the workpiece  102  by the machine tool  134  during the machining operation. 
     The oscillating force  256  is an external, periodic force that is applied to the workpiece  102  by the machine tool  134  during the machining operation. The oscillating force  256  induces forced oscillations to occur in the workpiece  102 , which generate vibrations. It can be appreciated that when the frequency  260  of the oscillating force  256  applied to the workpiece  102  is near the natural frequency  250  of the workpiece  102 , or the portion  254  of the workpiece  102 , the amplitude of the oscillation becomes large. Therefore, using the damping apparatus  174  to modify the natural frequency  250  of the portion  254  of the workpiece  102  to be different than the frequency  260  of the oscillating force  256  reduces the amplitude of the oscillations and, thereby, reduces the machine-induced vibration in the workpiece  102 . 
     In one or more examples, the natural frequency  250  of the workpiece  102 , or at least a portion (e.g., portion  254 ) of the workpiece  102 , is modified or selectively controlled such that a modified natural frequency  252  of at least a portion of the workpiece  102  is within a desired or predetermined range of frequencies (e.g., frequency range). As such, the modified natural frequency  252  can be tuned based on placement of the damping apparatus  174 . For the purpose of the present disclosure, the modified natural frequency  252  refers to the natural frequency  250  of at least a portion of the workpiece  102  as modified and selectively controlled by the damping apparatus  174 . Generally, the natural frequency  250  of at least a portion of the workpiece  102  is selectively controlled by the damping apparatus  174  such that the modified natural frequency  252  of at least a portion of the workpiece  102  is within the desired frequency range that is suitable to reduce the machine-induced vibrations in the workpiece  102  resulting from the machining operation. 
     In one or more examples, the natural frequency  250  of the portion  254  of the workpiece  102  is modified such that the natural frequency  250  (e.g., modified natural frequency  252 ) of the portion  254  of the workpiece  102  is less than the frequency  260  of the oscillating force  256  applied to the workpiece  102  by the machine tool  134  during the machining operation. 
     In one or more examples, the natural frequency  250  of the portion  254  of the workpiece  102  is modified such that the natural frequency  250  (e.g., modified natural frequency  252 ) of the portion  254  of the workpiece  102  is less than approximately one-half of the frequency  260  of the oscillating force  256  applied to the workpiece  102  by the machine tool  134  during the machining operation. Selectively controlling the natural frequency  250  such that the modified natural frequency  252  of at least a portion (e.g., portion  254 ) of the workpiece  102  is less than approximately one-half of the frequency  260  of the oscillating force  256  applied to the workpiece  102  provides the desired frequency range enables selective control (e.g., reduction) of the machine-induced vibrations. 
     In one or more examples, the natural frequency  250  of the portion  254  of the workpiece  102  is modified such that the natural frequency  250  of the portion  254  of the workpiece  102  is less than approximately one-third of the frequency  260  of the oscillating force  256  applied to the workpiece  102  by the machine tool  134  during the machining operation. Selectively controlling the natural frequency  250  such that the modified natural frequency  252  of at least a portion (e.g., portion  254 ) of the workpiece  102  is less than approximately one-third of the frequency  260  of the oscillating force  256  applied to the workpiece  102  provides the desired frequency range enables selective control (e.g., further reduction) of the machine-induced vibrations. 
     Referring now to  FIGS.  3 - 5  and  7   , in one or more examples, the damping apparatus  174  includes a fixture base  198  and a plurality of grippers  200 . Each one of the grippers  200  is coupled to the fixture base  198 . Each one of the grippers  200  is selectively movable (e.g., selectively extendable and retractable) relative to the fixture base  198 . For example, each one of the grippers  200  is configured to selectively extend or retract relative to the fixture base  198  such that one or more of the grippers  200  contacts and connects to the workpiece  102 , such as to a portion of the first surface  144  of the workpiece  102 . Connection of one or more of the grippers  200  to the workpiece  102  selectively controls or modifies the natural frequency  250  of the workpiece  102 . In other words, selective extension and retraction of the grippers  200  enables connection of select ones of the grippers  200  to the workpiece  102 , thereby, enabling selective control of the natural frequency  250  of the workpiece  102 . 
     In one or more examples, extension of select ones of the grippers  200  also enables connection to the workpiece  102  at locations on a surface of the workpiece  102  where a shape or contour of the surface of the workpiece  102  is compatible or suitable for mating and connection by the grippers  200 . Similarly, retraction of select ones of the grippers  200  also enables the damping apparatus  174  to avoid locations on the surface where a shape, contour, or other feature of the surface of the workpiece  102  is incompatible or difficult for mating and connection by the grippers  200 . 
     Referring now to  FIG.  8   , in one or more examples, the natural frequency  250  ( FIG.  1   ) of the portion  254  of the workpiece  102  is selectively controlled or modified by selecting one or more locations  222  of the portion  254  of the workpiece  102  (e.g., on the first surface  144 ) and selectively connecting one or more of the grippers  200  to the workpiece  102  at the one or more locations  222  (e.g., as shown in  FIG.  12   ). 
     In one or more examples, an intensity supplied by each one of the grippers  200  in contact with and connected to the workpiece  102  can be varied or selectively controlled to effectuate a desired change in a local or global frequency of the workpiece  102 . 
     Referring now to  FIGS.  2  and  8   , in one or more examples, the system  100  includes a computing device  110 . The computing device  110  is adapted to manipulate data representing the workpiece  102  and data representing the damping apparatus  174  and/or the workpiece holders  106 . The computing device  110  is also adapted to provide operating instructions to the damping apparatus  174 , the workpiece holders  106  and/or the machine tool  134 . 
     In one or more examples, the damping of machine-induced vibrations and the natural frequency  250  if the workpiece  102  is modified or selectively controlled dependent upon a measured frequency as different machining operations are performed at different locations on the workpiece  102  and/or from workpiece  102  to workpiece  102 . In one or more examples, the damping of machine-induced vibrations and the natural frequency  250  if the workpiece  102  is customized to each workpiece  102  and/or for a particular location on or portion of the workpiece  102 . 
     In one or more examples, the workpiece holders  106  are selectively controlled (e.g., by instructions provided by the computing device  110 ) to index the workpiece  102  within one of the work cells  226  (e.g., the second work cell  230 ). For example, the computing device  110  is programmed with an indexed position of the workpiece  102  based on a virtual indexed position of a digital model (e.g., a nominal model or an as-built model) of the workpiece  102  in the second work cell  230 . The computing device  110  is operable to instruct the workpiece holders  106  to move the workpiece  102  to the indexed position. 
     In one or more examples, the workpiece holders  106  are selectively controlled (e.g., by instructions provided by the computing device  110 ) to conform the workpiece  102  to the desired shape (e.g., the as-built shape). For example, the computing device  110  is programmed with the numerical control locations for each one of the numerical control contacts  136  and the shaping force applied to the workpiece  102  by the each one of the force control contacts  138 , for example, based on a digital model (e.g., a nominal model or an as-built model) of the workpiece  102 . The computing device  110  is operable to instruct the workpiece holders  106  to selectively extend or retract corresponding ones of the numerical control contacts  136  and the force control contacts  138  to conform the workpiece  102  to the desired shape or otherwise control the shape of the workpiece  102  as held by the workpiece holders  106 . 
     Referring briefly to  FIGS.  1  and  2   , in one or more examples, the workpiece  102  (e.g., a composite workpiece) is digitized while on the tool  150  (e.g., as shown in  FIG.  1   ) to capture an as-built shape of the workpiece  102 . In one or more examples, the as-built model  116  (e.g.,  FIG.  2   ) is generated that represents the workpiece  102  in the as-built shape. 
     In one or more examples, an initial processing operation (e.g., a machining, drilling, or trimming operation) may be performed on the workpiece  102 , for example, while the workpiece  102  is on the tool  150  (e.g., in the first work cell  228 ). In these examples, the workpiece  102  is digitized after the initial processing operation. As such, the as-built model  116  may also represent initially machined features of the workpiece  102 . In one or more examples, the workpiece  102  is removed from the tool  150  and is transported from the first work cell  228  to the workpiece holders  106  of the second work cell  230  for performance of a subsequent processing operation. 
     In one or more examples, the metrology system  108  is associated with, or forms a portion of, the first work cell  228 . In one or more examples, the metrology system  108  is movable into the first work cell  228 . In one or more examples, at least a portion of the metrology system  108  is positioned in the second work cell  230 . 
     In one or more examples, the metrology system  108  digitizes the workpiece  102 , for example, while the workpiece  102  is on the tool  150 . In one or more examples, the metrology system  108  generates measurement data  132  (e.g., as shown in  FIG.  2   ) for the workpiece  102 . In one or more examples, the measurement data  132  represents at least a portion of the workpiece  102 , for example, while the workpiece  102  is on the tool  150 , having the as-built shape. Accordingly, the measurement data  132  may also be referred to as as-built measurement data. In an example, the metrology system  108  digitizes at least the second surface  220  of the workpiece  102  such that the measurement data  132  represents the shape, contour, and features (e.g., edges, holes, etc.) of the second surface  220  of the workpiece  102 . 
     In one or more examples, the measurement data  132  is used to generate the as-built model  116  (e.g., as shown in  FIG.  2   ) that is representative of the workpiece  102 . In one or more examples, the computing device  110  is adapted to manipulate the scan data representing the workpiece  102  (e.g., measurement data  132 ) and/or to generate models representing the workpiece  102  (e.g., the as-built model  116 ) based on the scanned measurement data generated by the metrology system  108 . 
     Referring to  FIG.  2   , in one or more examples, the computing device  110  is operable to determine (e.g., approximate) the natural frequency  250  of the workpiece  102 , such as of the portion  254  of the workpiece  102 . In one or more examples, the computing device  110  determines the natural frequency  250  of the workpiece  102  (e.g., the portion  254 ) by analyzing a real-time model  112  ( FIG.  2   ) of the workpiece  102 , for example, as held and/or conformed by the workpiece holders  106 . 
     For the purpose of the present disclosure, the term “real-time,” such as in reference to a real-time condition or a real-time shape of the workpiece  102 , refers to an immediate or present condition of the workpiece  102  at a point in time in which the workpiece  102  has a shape (e.g., geometry, profile, contour, structural features, and the like) as presently positioned, such as before or during a processing operation (e.g., one or more machining operations). 
     Referring now to  FIGS.  2 ,  4  and  6   , in one or more examples, the metrology system  108  is associated with, or forms a portion of, at least one of the work cells  226 . In one or more examples, the metrology system  108  is movable into the second work cell  230 . In one or more examples, at least a portion of the metrology system  108  is positioned in the second work cell  230 . 
     In one or more examples, the metrology system  108  digitizes the workpiece  102 , for example, while the workpiece  102  is held in the second work cell  230  by the workpiece holders  106 , for example, in an indexed position and conformed to the desired shape. In one or more examples, the metrology system  108  generates the measurement data  132  (e.g., as shown in  FIG.  2   ) for the workpiece  102 . In one or more examples, the measurement data  132  represents at least a portion of the workpiece  102  while the workpiece  102  is positioned (e.g., indexed) in the second work cell  230  by the workpiece holders  106  and has the desired shape, for example, as held by the workpiece holders  106 . Accordingly, the measurement data  132  may also be referred to as real-time measurement data. 
     In an example, the metrology system  108  digitizes at least the first surface  144  of the workpiece  102  such that the measurement data  132  represents the shape, contour, and features (e.g., edges, holes, etc.) of the first surface  144  of the workpiece  102 . In another example, the metrology system  108  digitizes at least the second surface  220  of the workpiece  102  such that the measurement data  132  represents the shape, contour, and features (e.g., edges, holes, etc.) of the second surface  220  of the workpiece  102 . In yet another example, the metrology system  108  digitizes the first surface  144  and the second surface  220  of the workpiece  102  such that the measurement data  132  represents the shape, contour, and features (e.g., edges, holes, etc.) of the first surface  144  and the second surface  220  of the workpiece  102 . 
     In one or more examples, the measurement data  132  is used to generate the real-time model  112  (e.g., as shown in  FIG.  2   ) that is representative of the workpiece  102 . In one or more examples, the computing device  110  is adapted to manipulate the scan data representing the workpiece  102  (e.g., measurement data  132 ) and/or to generate models representing the workpiece  102  (e.g., the real-time model  112 ) based on the scanned measurement data generated by the metrology system  108 . 
     In one or more examples, the metrology system  108  includes a scanner  264  (e.g., as shown in  FIGS.  5  and  6   ). In one or more examples, the metrology system  108  includes more than one scanner. For example, the scanner  264  (e.g., one or more scanners) are associated with or are positioned in each one of the work cells  226 . 
     The scanner  264  scans and digitizes at least a portion of the workpiece  102 . In one or more examples, the scanner  264  is any one of various types of three-dimensional (3D) scanners. In one or more examples, the scanner  264  includes, or is, a photogrammetric scanner, such as a photogrammetric camera. In other examples, the scanner  264  includes, or is, one of a laser triangulation scanner, a structured light scanner, other laser-based scanners or metrology systems, and the like. 
     In one or more examples, the scanner  264  of the metrology system  108  captures the geometry (e.g., size and shape), contour (e.g., curvature), physical features (e.g., holes, edges, etc.), and other details of the workpiece  102 . Scan data (e.g., measurement data  132 ) generated the scanner  264  is used by a computer (e.g., the computing device  110 ) to generate a model of the workpiece  102  (e.g., the real-time model  112 , the as-built model  116 , etc.). The model of the workpiece  102  is a digital three-dimensional representation of the workpiece  102 . 
     In one or more examples, the computing device  110  is operable to compare the real-time model  112  to the as-built model  116  (or a nominal model of the workpiece  102 ) of the workpiece  102 . For example, the computing device  110  is adapted to perform various transforms (e.g., rigid body transforms and/or coordinate frame transforms) and/or other data manipulation operations (e.g., global best fit operations) to virtually compare the real-time model  112  to the as-built model  116 . 
     In one or more examples, comparison of the real-time model  112  to the as-built model  116  determines whether the workpiece  102  is appropriately indexed in the second work cell  230 . In situations where the comparison of the real-time model  112  to the as-built model  116  indicates that the workpiece  102  is not appropriately indexed, the computing device  110  is operable to instruct the workpiece holders  106  to adjust the position of the workpiece  102  in the second work cell  230  based on the comparison, such that the workpiece  102  is appropriately indexed. 
     In one or more examples, comparison of the real-time model  112  to the as-built model  116  determines whether the workpiece  102  is conformed to the desired shape in the second work cell  230 . In situations where the comparison of the real-time model  112  to the as-built model  116  indicates that the workpiece  102  is not conformed to the desired shape, the computing device  110  is operable to instruct the workpiece holders  106  to adjust the clamp  120  (e.g., modify the position and/or orientation of the clamp  120  relative to the workpiece  102 , modify the location of the second jaw  126  relative to the first jaw  122 , modify the numerical control location of one or more of the numerical control contacts  136 , etc.) based on the comparison, such that the workpiece  102  is conformed to the desired shape. 
     In one or more examples, the computing device  110  determines (e.g., approximates) the natural frequency  250  of the workpiece  102  with the workpiece  102  held by the workpiece holders  106  (e.g., in the indexed position and conformed to the desired shape). In other examples, the computing device  110  determines (e.g., approximates) the natural frequency  250  of the workpiece  102  (e.g., the portion  254 ) by analyzing additional data and/or other information representing the workpiece  102 , such as the geometry, mass, and stiffness of the workpiece  102  (e.g., the portion  254 ), the locations of the workpiece holders  106  relative to the workpiece  102  (e.g., the location and orientation of the clamp  120  on the workpiece  102 ), the distance between the adjacent pair of workpiece holders  106 , and the like. 
     In one or more examples, a frequency of the machine-induced vibrations in the workpiece  102  is measured during the machining operation performed by the machine tool  134 . The computing device  110  is adapted to analyze the measured frequency at different locations on the workpiece  102  and determine (e.g., calculate) a modification for the natural frequency  250  (e.g., modified natural frequency  252 ) of the workpiece  102  needed to reduce the machine- induced vibrations, for example, by selecting locations for connection of select ones of the grippers  200 , the number of grippers  200  to be connected to the workpiece  102 , and the like, thereby increasing the mass  103  and/or the stiffness  105  of at least a portion (e.g., portion  254 ) of the workpiece  102 . 
     Referring again to  FIGS.  2  and  8   , in one or more examples, the computing device  110  is further operable to select the one or more locations  222  on the workpiece  102 , such as on the portion  254  of the workpiece  102 , for connection of the one or more of the grippers  200 . The locations  222  for connection of the grippers  200  are selected such that the modified natural frequency  252  ( FIG.  2   ) of the workpiece  102 , such as of the portion  254  of the workpiece  102 , is less than the frequency  260  of the oscillating force  256  applied to the workpiece  102  by the machine tool  134  during the machining operation. 
     In one or more examples, the locations  222  on the workpiece  102  are extracted, calculated, or otherwise determined from the real-time model  112  ( FIG.  2   ) and analysis of the natural frequency  250  of the workpiece  102 . In one or more examples, selection of the locations for coupling select ones of the grippers  200  based on the analysis of the natural frequency  250  and the frequency  260  of the oscillating force  256  applied to the workpiece  102  by the machine tool  134  (e.g., the machine-induced vibrations resulting from the machining operation) enables the modified natural frequency  252  to be tuned to a desired frequency or frequency range. 
     Referring now to  FIGS.  7 - 12   , in one or more examples, the damping apparatus  174  has any number of the grippers  200 . The grippers  200  may be arranged in any desirable configuration or pattern, such as in an array of rows. In one or more examples, each one of the grippers  200  (e.g., identified individually as a gripper  258  as shown in  FIGS.  8 - 12   ) includes a linear actuator  202  and a vacuum cup  204 . The vacuum cup  204  is coupled to the linear actuator  202 . The gripper  258  illustrated in  FIGS.  9 - 12    is an example of any one of the grippers  200  (e.g., as shown in  FIGS.  8  and  9   ). 
     In one or more examples, the linear actuator  202  includes an outboard end that is linearly movable relative to the fixture base  198  along a movement axis. The vacuum cup  204  is located at (e.g., coupled to) the outboard end of the linear actuator  202 . As such, the linear actuator  202  linearly moves the vacuum cup  204  relative to the fixture base  198  along the movement axis into selective contact with a surface (e.g., the first surface  144 ) of the workpiece  102  (e.g., as shown in  FIGS.  9 - 11   ). 
     The vacuum cup  204  is configured to grip the workpiece  102  using vacuum. For example, with the vacuum cup  204  in contact with the surface of the workpiece  102 , the vacuum cup  204  grips the workpiece  102  using a vacuum formed between the vacuum cup  204  and the surface of the workpiece  102 . Upon activation of the vacuum, the vacuum cup  204  provides a holding force that is sufficient to hold the workpiece  102  in a fixed position. 
     With the vacuum formed between the vacuum cup  204  and the surface of the workpiece  102 , the linear actuator  202  is configured to lock linear movement of and, thus, lock a linear position of the vacuum cup  204  along the movement axis. As used herein, “lock” and “locking,” for example, in reference to movement and/or position, refers to immobilizing or making the element to which the term refers immovable. 
     Generally, gripping the workpiece  102  at the locations  222  with the grippers  200  holds the workpiece  102  in a rigidly fixed position between the adjacent pair of workpiece holders  106 , which modifies the natural frequency  250  of the workpiece  102  and prevents, or greatly reduces, vibration in the workpiece  102  during the machining operation. In one or more examples, with linear movement of the gripper  258  locked, the outboard end of the linear actuator  202  and the vacuum cup  204  support the workpiece  102  from behind (e.g., backs up the portion  254  of the workpiece  102 ), opposite to a machining load applied to the workpiece  102  by the machine tool  134 , during the machining operation. Accordingly, with the grippers  200  coupled to the workpiece  102  at the locations  222  (e.g., as shown in  FIG.  8   ), the mass  103  and/or stiffness  105  of the portion  254  of the workpiece  102  is increased at the associated one of the locations  222 . 
     Referring to  FIGS.  9 - 11   , in one or more examples, the linear actuator  202  moves through a range of movement, for example, between a first position  268  (e.g., as shown in  FIG.  9   ) and a second position  270  (e.g., as shown in  FIG.  10   ). Movement of the linear actuator  202  similar moves the vacuum cup  204  between the first position  268  and the second position  270 . The first position  268  refers to any position in which the vacuum cup  204  is not in contact with the workpiece  102  and may be referred to as an unactuated position, a rest position, a retracted position, or a noncontact position. The second position  270  refers to a position in which the vacuum cup  204  is in contact with the workpiece  102  and may be referred to as an actuated position, an extended position, or a contact position. 
     In one or more examples, with the linear actuator  202  in the second position  270  (e.g., as shown in  FIG.  10   ), a negative pressure generated by the vacuum formed between the vacuum cup  204  and the surface (e.g., first surface  144 ) of the workpiece  102  moves the linear actuator  202  through a range of motion from the second position  270  to a third position  272  (e.g., as shown in  FIG.  11   ). The third position  272  refers to a position in which the vacuum cup  204  is coupled to the workpiece  102  and may be referred to as a locked position. 
     In an example, the linear actuator  202  selectively, linearly moves (e.g., extends) the vacuum cup  204  relative to the fixture base  198  and to the surface of the workpiece  102  along the movement axis from the first position  268  (e.g., unactuated position shown in  FIG.  9   ) to the second position  270  (e.g., actuated position shown in  FIG.  10   ) in which the vacuum cup  204  is in contact with the surface of the workpiece  102 . With the vacuum cup  204  in contact with the surface of the workpiece  102  (e.g., as shown in  FIG.  10   ), the linear actuator  202  is configured to enable free linear movement along the movement axis. As used herein, free linear movement refers to unrestricted or unobstructed movement of the element to which the term refers. The vacuum formed between the vacuum cup  204  and the surface of the workpiece  102  urges further linear movement (e.g., extension) of the linear actuator  202  along the movement axis into the third position  272  (e.g., the locked position as shown  FIG.  11   ). With the linear actuator  202  in the third position  272 , the linear actuator  202  is further configured to fix linear movement along the movement axis, thereby fixing the vacuum cup  204  in the third position  272  (e.g., as shown in  FIG.  11   ). 
     The vacuum formed between the vacuum cup  204  and the surface of the workpiece  102  securely holds the workpiece  102  and couples the workpiece  102  to the damping apparatus  174 . Linear movement (e.g., extension) of linear actuator  202  toward the workpiece  102 , rather than movement of the workpiece  102  toward the linear actuator  202 , in response to the negative pressure generated by the vacuum, prevents inducing an undesirable load in the workpiece  102 . Additionally, fixing the linear position of the linear actuator  202  in the third position  272  supports the workpiece  102 , thus, modifying the natural frequency  250  of the workpiece  102 . 
     Referring now to  FIGS.  2  and  9 - 12   , in one or more examples, the gripper  258  (e.g., each one of the grippers  200 ) also includes an actuator control unit  208 . In one or more examples, the actuator control unit  208  controls linear movement (e.g., extension and retraction) of the linear actuator  202  to place the vacuum cup  204  in contact with the workpiece  102 . In one or more examples, the actuator control unit  208  also controls application of the vacuum. 
     In one or more examples, the gripper  258  (e.g., each one of the grippers  200 ) includes a power-transmitting component  212  (e.g., as shown in  FIGS.  2  and  12   ). The power-transmitting component  212  drives linear movement (e.g., extension and retraction) of the linear actuator  202 , for example, under direction from the actuator control unit  208 . In one or more examples, the power-transmitting component  212  is operatively coupled to a power source  278  (e.g., as shown in  FIG.  12   ). 
     In one or more examples, the gripper  258  (e.g., each one of the grippers  200 ) also includes an actuator stop-lock  210 . The actuator stop-lock  210  selectively locks a position of the linear actuator  202 , for example, under direction from the actuator control unit  208 . For example, the actuator stop-lock  210  is operable to fix, or lock, the outboard end of the linear actuator  202  and, thus, the vacuum cup  204  in the third position  272  (e.g., as shown in  FIG.  11   ). In one or more examples, the actuator stop-lock  210  is operatively coupled with the power-transmitting component  212  to lock linear movement of the linear actuator  202  along the movement axis, for example, when the linear actuator  202  is in the third position  272 . 
     Referring briefly to  FIG.  12   , in one or more examples, the linear actuator  202  includes a stationary member  274  that is coupled to the fixture base  198  and a movable member  276  that is coupled to the stationary member  274 . The movable member  276  is linearly movable relative to the stationary member  274  along the movement axis. A free end of the movable member  276  defines the outboard end of the linear actuator  202 . 
     In one or more examples, the power-transmitting component  212  is operatively coupled with the power source  278  and with the stationary member  274  and the movable member  276 . The power-transmitting component  212  is operable to selectively drive linear movement of (e.g., extend) the movable member  276  relative to the stationary member  274  along the movement axis, for example, from the first position  268  (e.g., as shown in  FIG.  9   ) to the second position  270  (e.g., as shown in  FIG.  10   ). Once in the second position  270 , with the vacuum cup  204  in contact with the surface of the workpiece  102 , the power-transmitting component  212  is configured to enable free linear movement of the movable member  276  relative to the stationary member  274 . The vacuum created by the vacuum cup  204  linearly moves (e.g., further extends) the movable member  276  from the second position  270  to the third position  272  (e.g., as shown in  FIG.  11   ). The actuator stop-lock  210  is operatively coupled with the power-transmitting component  212  to lock linear movement of the movable member  276  relative to the stationary member  274  along the movement axis, for example, when the linear actuator  202  is in the third position  272 . 
     In one or more examples, the actuator control unit  208  selectively controls linear movement of the linear actuator  202  via control of the power source  278 , control of the power-transmitting component  212 , and/or control of the actuator stop-lock  210 . In one or more examples, the actuator control unit  208  selectively controls application of the vacuum applied by the vacuum cup  204 , for example, via control of a vacuum source  280 . In one or more examples, the system  100  also includes at least one power supply (not shown) that provides power, as needed, to the various components of the system  100 . 
     Referring still to  FIG.  12   , in one or more examples, the gripper  258  (e.g., each one of the grippers  200 ) includes a pivot coupling  266 . The pivot coupling  266  pivotally couples the outboard end of the linear actuator  202  and the vacuum cup  204  together. The pivot coupling  266  enables the vacuum cup  204  to pivot relative to the linear actuator  202  about at least one pivot axis. In an example, the movement axis extends through the pivot coupling  266 . In an example, the pivot axis is perpendicular to the movement axis. The vacuum cup  204  being pivotable relative to the linear actuator  202  enables self-adjustment of an angular orientation of the vacuum cup  204  relative to the workpiece  102  to accommodate for different shapes and/or contours of the portion  254  of the workpiece  102 . 
     Referring again to  FIGS.  2  and  9 - 12   , in one or more examples, the actuator control unit  208  causes engagement of (e.g., activates or energizes) the power-transmitting component  212  to extend the linear actuator  202  from the first position  268  (e.g., as shown in  FIG.  9   ) to the second position  270  (e.g., as shown in  FIG.  10   ), which places the vacuum cup  204  in contact with the workpiece  102 . Upon contact of vacuum cup  204  with the workpiece  102 , the actuator control unit  208  causes disengagement of (e.g., deactivates or deenergizes) the power-transmitting component  212  to enable free extension of the linear actuator  202 . With the vacuum cup  204  in contact with the workpiece  102  and the power-transmitting component  212  disengaged, the actuator control unit  208  applies the vacuum to further extend the linear actuator  202  from the second position  270  to the third position  272  (e.g., as shown in  FIG.  11   ). With the vacuum formed between the vacuum cup  204  and the workpiece  102  and the power-transmitting component  212  disengaged, the actuator control unit  208  engages the actuator stop-lock  210  to lock the linear actuator  202  in the third position  272 . 
     In one or more examples, the linear actuator  202  is a hydraulic linear actuator, the power source  278  is a hydraulic pump, and the power-transmitting component  212  is pressurized hydraulic fluid. In these examples, the stationary member  274  includes a hollow cylinder and the movable member  276  includes a piston located inside the hollow cylinder and a piston rod coupled to the piston (e.g., a free end of the piston rod defines the outboard end of the linear actuator  202 ). The pressurized hydraulic fluid within the hollow cylinder acts on the piston and drives linear movement of the piston. The actuator stop-lock  210  is a hydraulic valve that is operable to close off the hydraulic system and hydrostatically lock the hydraulic actuator. 
     In one or more examples, the linear actuator  202  is a pneumatic linear actuator, the power source  278  is a compressor, and the power-transmitting component  212  is pressurized gas (e.g., air). In these examples, the stationary member  274  includes a hollow cylinder and the movable member  276  includes a piston located inside the hollow cylinder and a piston rod coupled to the piston (e.g., a free end of the piston rod defines the outboard end of the linear actuator  202 ). The pressurized gas within the hollow cylinder acts on the piston and drives linear movement of the piston. The actuator stop-lock  210  is a pneumatic valve that is operable to close off the pneumatic system and lock the pneumatic actuator. 
     In one or more examples, the linear actuator  202  is a mechanical or electromechanical linear actuator, the power source  278  is a motor, and the power-transmitting component  212  includes a drive mechanism that operates to convert rotary motion of the motor into linear motion of the movable member  276  (e.g., a screw drive, a rack and pinion drive, a chain drive, a belt drive, and the like). In these examples, the stationary member  274  includes a hollow housing and the movable member  276  includes a rod (e.g., a free end of the rod defines the outboard end of the linear actuator  202 ). The drive mechanism within the hollow housing acts on the rod and drives linear movement of the rod. The actuator stop-lock  210  is a mechanical rod lock that is operable to restrict operation of the drive mechanism. 
     In one or more examples, the vacuum source  280  is coupled to (e.g., in fluid communication with) the vacuum cup  204 . In one or more examples, the vacuum source  280  includes least one vacuum generator that is coupled to (e.g., in fluid communication with) the vacuum cup  204 , such as via at least one air line (e.g., hose or tube) that directs a flow of air and at least one air supply valve that controls the flow of air. In an example, the air supply valve is an electrically controlled solenoid valve that is operatively coupled with and commanded by the actuator control unit  208  and/or the computing device  110 . 
     In one or more examples, the power source  278  and/or the vacuum source  280  are dedicated to each one of the grippers  200 . In other examples, the power source  278  and/or the vacuum source  280  are shared by more than one of the grippers  200 . In these examples, the system  100  includes at least one vacuum supply manifold and/or at least one power supply manifold that distributes vacuum and/or power to more than one of the grippers  200 . 
     Similarly, in one or more examples, the actuator control unit  208  is dedicated to each one of the grippers  200 . In other examples, the actuator control unit  208  is shared by more than one of the grippers  200 . 
     Referring now to  FIGS.  2  and  12   , in one or more examples, the gripper  258  (e.g., each one of the grippers  200 ) includes a sensor  206 . The sensor  206  is configured or is operable to determine when the linear actuator  202  is in the second position  270 . In one or more examples, the sensor  206  detects contact of the vacuum cup  204  with the workpiece  102 . In one or more examples, the sensor  206  is located at the outboard end of the linear actuator  202 . In one or more examples, the sensor  206  is located proximate to the vacuum cup  204 . 
     In one or more examples, the sensor  206  is a position sensor that is operable to detect a position of the outboard end of the linear actuator  202 . In one or more examples, the sensor  206  is a contact sensor that is operable to detect when the vacuum cup  204  is in contact with the workpiece  102 . In one or more examples, the sensor  206  is a proximity sensor that is operable to detect when the linear actuator  202  (e.g., the outboard end) is near the workpiece  102 . Any other suitable type of sensor is also contemplated. 
     In one or more examples, once the sensor  206  detects that the vacuum cup  204  is in contact with the surface of the workpiece  102  and/or that the linear actuator  202  is in the second position  270  (e.g., as shown in  FIG.  10   ), the linear actuator  202  is commanded to cease linear movement (e.g., extension). Once selectively controlled linear movement (e.g., extension) of the linear actuator  202  has stopped, the linear actuator  202  disengages or releases to enable free linear movement (e.g., extension). The vacuum is then applied to the surface of the workpiece  102  by the vacuum cup  204  to grip the workpiece  102 . The vacuum draws, or otherwise pulls, the linear actuator  202  toward the workpiece  102  and positions the linear actuator  202  in the third position  272  (e.g., as shown in  FIG.  11   ). 
     In one or more examples, the sensor  206  is coupled to or is in communication with the actuator control unit  208  and/or the computing device  110 . In one or more examples, the actuator control unit  208  selectively controls linear movement of the linear actuator  202  via control of the power source  278 , control of the power-transmitting component  212 , and/or control of the actuator stop-lock  210  based on signals from the sensor  206  indicative of the position of the of the linear actuator  202 . 
     Referring to  FIG.  7   , in one or more examples, each one of the grippers  200  includes a bellows cover  214 . The bellows cover  214  surrounds at least a portion of the linear actuator  202  that is located external to the fixture base  198 . The bellows cover  214  is configured to enable linear movement (e.g., extension and retraction) of the linear actuator  202 . The bellows cover  214  protects the linear actuator  202  and prevents debris (e.g., from the machining operation) from interacting with the linear actuator  202 . 
     Referring now to  FIGS.  3 - 7   , in one or more examples, the damping apparatus  174  (e.g., each one of the damping apparatuses  104 ) is movable in or relative to one of the work cells  226  (e.g., the second work cell  230 ) and/or relative to the workpiece  102 . In an example, the damping apparatus  174  is linearly moveable along at least one axis to move and locate the grippers  200  relative to the workpiece  102 . In another example, the damping apparatus  174  is rotationally movable along at least one axis to move and orient the grippers  200  relative to the workpiece  102 . 
     Referring to  FIG.  7   , in one or more examples, the fixture base  198  includes a pedestal  216  and a stanchion  218 . The stanchion  218  is coupled to the pedestal  216 . The grippers  200  are coupled to and are moveable (e.g., extend and retract) relative to the stanchion  218 . 
     In one or more examples, the fixture base  198  is movable in the second work cell  230  and relative to the workpiece  102 . Generally, movement of the fixture base  198  relative to the workpiece  102  also moves the grippers  200  relative to the workpiece  102  (e.g., relative to the first surface  144 ) of the workpiece  102 , thereby selectively positioning the grippers  200  relative to a connecting surface (e.g., first surface  144 ) of the workpiece  102 . For example, movement of the fixture base  198  selectively moves and positions the grippers  200  in at least one of a horizontal or vertical direction relative to the first surface  144  of the workpiece  102  (e.g., in a chordwise direction and/or a spanwise direction of a wing panel). In one or more examples, movement of the fixture base  198  relative to the workpiece  102  enables connection of the grippers  200  to the workpiece  102  at locations on a surface of the workpiece  102  where a shape or contour of the surface of the workpiece  102  is compatible or suitable for mating and connection by the grippers  200  and avoidance at locations on the surface where a shape, contour, or other feature of the surface of the workpiece  102  is incompatible or difficult for mating and connection by the grippers  200 . 
     In one or more examples, the stanchion  218  is movable relative to the pedestal  216 . In an example, the stanchion  218  is linearly moveable along at least one axis relative to the pedestal  216  to move and locate the grippers  200  relative to the workpiece  102 . In another example, the stanchion  218  is rotationally movable along at least one axis relative to the pedestal  216  to move and orient the grippers  200  relative to the workpiece  102 . 
     In one or more examples, the pedestal  216  is movable in a corresponding one of the work cells  226  (e.g., the second work cell  230 ) relative to the workpiece  102 . In an example, the pedestal  216  is linearly moveable along at least one axis to move and locate the stanchion  218  relative to the workpiece  102 . In another example, the pedestal  216  is rotationally movable along at least one axis to move and orient the stanchion  218  relative to the workpiece  102 . 
     The principles and implementations of the system  100  disclosed herein enable the digital model to be updated after a machining operation is performed, such that the digital model is representative of an as-machined shape of the workpiece  102 . The updated digital model of the workpiece  102  (e.g., in the as-machined shape) may be used to index the workpiece  102  before a subsequent processing operation is performed on the workpiece  102 . The updated digital model of the workpiece  102  may also be used to conform the workpiece  102  to the desired shape (e.g., an as-machined shape) during a subsequent processing operation performed on the workpiece  102 . The updated digital model of the workpiece  102  may also be used to determine the natural frequency  250  of the workpiece  102  and to select the locations  222  on the workpiece  102  for coupling of the grippers  200  of the damping apparatus  174 , which modify the natural frequency  250  to dampen the machine-induced vibrations. As such, the principles of the system  100  disclosed herein also enable determinant assembly or predictive assembly of the workpiece  102  based on the digital model of the workpiece  102 , which is updated throughout processing of the workpiece  102 . 
     Referring now to  FIG.  6   , in one or more examples, the metrology system  108  digitizes the workpiece  102 , for example, during and/or after performing the processing operation and while the workpiece  102  is held by the workpiece holders  106  and coupled to the damping apparatus  174 . In one or more examples, the metrology system  108  generates the measurement data  132  (e.g., as shown in  FIG.  2   ) for the workpiece  102 . In one or more examples, the measurement data  132  represents at least a portion of the workpiece  102  after the machining operation, for example, performed by the machine tool  134 . Accordingly, the measurement data  132  may also be referred to as as-machined measurement data. 
     In an example, the metrology system  108  digitizes at least the first surface  144  of the workpiece  102  such that the measurement data  132  represents the shape, contour, previous features (e.g., prior formed edges, holes, etc.) and newly added features (e.g., newly formed edges, holes, etc.) of the first surface  144  of the workpiece  102 . In another example, the metrology system  108  digitizes at least the second surface  220  of the workpiece  102  such that the measurement data  132  represents the shape, contour, previous features (e.g., prior formed edges, holes, etc.) and newly added features (e.g., newly formed edges, holes, etc.) of the second surface  220  of the workpiece  102 . In yet another example, the metrology system  108  digitizes the first surface  144  and the second surface  220  of the workpiece  102  such that the measurement data  132  represents the shape, contour, previous features (e.g., prior formed edges, holes, etc.) and newly added features (e.g., newly formed edges, holes, etc.) of the first surface  144  and the second surface  220  of the workpiece  102 . 
     In one or more examples, the measurement data  132  is used to update the digital model of workpiece  102  (e.g., the as-built model  116 ) or to generate an as-machined model  180  (e.g., as shown in  FIG.  2   ) that is representative of the workpiece  102  having the as-machined shape. Accordingly, the as-machined model  180  represents an update to the as-built model  116 , which includes features formed during the machining operation. In one or more examples, the computing device  110  is adapted to manipulate the scan data representing the workpiece  102  (e.g., measurement data  132 ) and/or to generate models representing the workpiece  102  (e.g., the as-machined model  180 ) based on the scanned measurement data generated by the metrology system  108 . 
     It can be appreciated that this process implemented by the system  100 , as described herein and illustrated in  FIGS.  2 - 12   , may be repeated any number of times as the workpiece  102  moves through the other work cells  226  of the manufacturing environment  224 . For example, workpiece holders  106  associated with each one of the work cells  226  hold the workpiece  102  during performance of a subsequent processing operation, index the workpiece  102  before performing the subsequent processing operation, and/or conform the workpiece  102  to the desired shape before performing the subsequent processing operation. The damping apparatuses  104  associated with each one of the work cells  226  connect to the workpiece  102  at the locations  222  selected to modify the natural frequency  250  of the workpiece  102  as desired to control (e.g., reduce) vibrations during the processing operation. Additionally, the as-machined model  180  may be generated or updated after each subsequent processing operation, such that, upon completion of all processing operations, the as-machined model  180  represents the workpiece  102  having the as-built shape and all the machined features. As such, the workpiece  102  fabricated in this manner may be used for determinant assembly or predictive assembly of another structure, such as the wing  1220  of the aircraft  1200  (e.g., as shown in  FIG.  15   ). 
     Referring again to  FIG.  1   , in one or more examples, the workpiece  102  is successively transported from one of the work cells  226  (e.g., the second work cell  230 ) to another one of the work cells  226  (e.g., the third work cell  232 ) for performance of subsequent processing operations. This process may be repeated any number of times to move the workpiece  102  through the work cells  226  and to perform any number of processing operations. The workpiece holders  106  and the damping apparatuses  104  may be used in any one of the work cells  226 , as described herein above and illustrated in  FIGS.  3 - 6   , to dampen machine-induced vibrations during a machining operation. 
     In one or more examples, the system  100  includes an overhead workpiece handler  166 . The overhead workpiece handler  166  is coupled to the workpiece  102 . The overhead workpiece handler  166  supports the workpiece  102  while transporting the workpiece  102  between the work cells  226 . 
     In one or more examples, with the workpiece  102  released from the workpiece holders  106 , the overhead workpiece handler  166  transports the workpiece  102  between the work cells  226  of the manufacturing environment  224 . For example, the overhead workpiece handler  166  transports the workpiece  102  from the second work cell  230 , following the processing operation, to the third work cell  232  for performance of a subsequent processing operation, and so on. In one or more examples, the overhead workpiece handler  166  carries the workpiece in the approximately vertical orientation. 
     Referring now to  FIGS.  4 - 6   , in one or more examples, the overhead workpiece handler  166  supports the workpiece  102  during the processing operation and while the workpiece  102  is held by the workpiece holders  106  and is coupled to the damping apparatus  174 . 
     In one or more examples, the overhead workpiece handler  166  includes a support beam  168  and a plurality of hangers  170 . The hangers  170  are connected to the support beam  168  and to the workpiece  102  such that the workpiece  102  is suspended from the support beam  168 , such as in the approximately vertical orientation. 
     In one or more examples, the hangers  170  are connected to the workpiece  102  at, or using, holes  248  machined in the workpiece  102 , such that the workpiece  102  is suspended from the hangers  170  by the holes  248 . In one or more examples, the holes  248  are machined through the workpiece  102  while the workpiece  102  is on the tool  150  (e.g., in the first work cell  228  as shown in  FIG.  1   ) and has the as-built shape. In one or more examples, the holes  248  are represented in the as-built model  116  and in the real-time model  112  and are used as alignment features during comparison (e.g., transform) of the real-time model  112  to the as-built model  116  for indexing the workpiece  102  and/or for conforming the workpiece  102  to the as-built shape. 
     Referring again to  FIG.  2   , in one or more examples, computing device  110  may include a single computer or several interconnected computers. For example, the computing device  110  may include any collection of computing devices that individually or jointly execute a set (or multiple sets) of instructions to implement any one or more of the operations discussed herein. The computing device  110  includes a processor  240  (e.g., at least one processing unit) that is coupled to memory  238 . The memory  238  includes program code  242  that is executable by the processor  240  to perform one or more operations. 
     Generally, as used herein, the phrase “the computing device  110  is adapted to” refers to the computing device  110  being configured or otherwise operable to perform a function, such as the program code  242  being executed by the processor  240  to perform a desired operation or function. The program code  242  is any coded instructions that is (e.g., computer readable and/or machine readable. The memory  238  is any a non-transitory computer readable and/or machine readable medium, such as a hard disk drive, flash memory, read-only memory, a compact disk, a digital versatile disk, a cache, random-access memory, and/or any other storage device or storage disk in which information is stored for any duration (e.g., for extended time periods, permanently, for brief instances, for temporarily buffering, and/or for caching of the information). 
     In one or more examples, the computing device  110  is adapted to perform various transforms (e.g., rigid body transforms and/or coordinate frame transforms) and/or other data manipulation operations (e.g., global best fit operations) to virtually compare digital models that are representative of the workpiece  102  (e.g., the real-time model  112 , the as-built model  116 , the as-machined model, etc.). These operations may be used to index the workpiece  102 , conform the workpiece  102  to the desired shape, and select the locations  222  for connection of the grippers  200  to modify the natural frequency  250  of the workpiece  102  as desired. 
     The present disclosure is also directed to a method for damping vibrations in the workpiece  102  using the system  100 . The present disclosure is further directed to the workpiece  102  manufactured using the system  100 . The present disclosure is additionally directed to the system  100  for damping vibrations in the workpiece  102  that includes the damping apparatus  174  (e.g., at least one of the damping apparatuses  104 ). The present disclosure is also directed to the damping apparatus  174 , such as the plurality of damping apparatuses  104 , for damping machine-induced vibrations in the workpiece  102 , for example, in at least one of the work cells  226  of the manufacturing environment  224  during a processing operation (e.g., a machining operation). 
     Referring generally to  FIGS.  1 - 12    and particularly to  FIG.  13   , by way of examples, the present disclosure is also directed to a method  1000  for damping vibrations in the workpiece  102 . In one or more examples, the method  1000  for damping vibrations in the workpiece  102  is implemented during, or forms a portion of, a method for processing or manufacturing the workpiece  102 . In one or more examples, the method  1000  for damping vibrations in the workpiece  102  is implemented during, or forms a portion of, a method for fabricating a portion of an aircraft  1200  (e.g., as shown in  FIG.  17   ). In one or more examples, the method  1000  is implemented using the system  100 . In one or more examples, the method  1000  is implemented using the damping apparatus  174 . 
     Generally, the method  1000  includes, or begins with, a step of forming the workpiece  102 . In one or more examples, the workpiece  102  is made or formed of a composite material (e.g., is a composite workpiece). In one or more examples, the workpiece  102  is made or formed of a metallic material (e.g., is a metallic workpiece). At this point in the fabrication process, the workpiece  102  may also be considered or referred to as a pre-cursor workpiece in which the workpiece  102  is in a condition prior to machining or post-formation processing operations being performed on the workpiece  102 . 
     In reference to a composite workpiece, the step of forming the workpiece  102  includes a step of forming a composite layup on a tool surface of the tool  150 . Alternatively, the method  1000  includes a step of forming the composite layup on a dedicate layup tool and a step of transferring the composite layup to the tool  150  for curing. The method  1000  also includes a step of curing the composite layup (e.g., an uncured or “green” composite) on the tool  150  to form the workpiece  102  (e.g., a cured composite workpiece). 
     In one or more examples, the method  1000  includes a step of performing at least one (e.g., an initial) processing operation on the workpiece  102 , for example, while the workpiece  102  (e.g., the composite workpiece) is on the tool  150 , having the as-built shape. For example, the holes  248  may be machined (e.g., drilled) through the workpiece  102 , while the workpiece  102  is on the tool  150  and has the as-built shape. 
     In one or more examples, the method  1000  includes a step of digitizing at least a portion of the workpiece  102  having the as-build shape. In one or more examples, the step of digitizing the workpiece  102  includes a step of generating the measurement data  132  (e.g., as-built measurement data) for the workpiece  102 . In one or more examples, the measurement data  132  is generated using the metrology system  108 . In one or more examples, the measurement data  132  is generated while the workpiece  102  is on the tool  150  and has the as-built shape. In one or more examples, the step of digitizing at least a portion of the workpiece  102  includes a step of generating the as-built model  116  using the measurement data  132 . 
     In reference to a composite workpiece, in one or more examples, the method  1000  includes a step of demolding the workpiece  102  from the tool  150 . In one or more examples, the step of demolding the workpiece  102  includes a step of separating the workpiece  102  from the tool surface and a step of removing the workpiece  102  from the tool  150 . In one or more examples, the step of demolding is preformed automatically or semi-automatically using a material handler. In one or more examples, the step of demolding is performed manually. 
     In one or more examples, the method  1000  includes a step of transporting the workpiece  102 . For example, the workpiece  102  is transported from one of the work cells  226  (e.g., the first work cell  228 ) to another one of the work cells  226  (e.g., the second work cell  230 ) of the manufacturing environment  224 . 
     In one or more examples, the workpiece  102  is transported from one of the work cells  226  (e.g., the first work cell  228 ) to another one of the work cells  226  (e.g., the second work cell  230 ) using a material handler. In one or more examples, the workpiece  102  is transported from one of the work cells  226  (e.g., the second work cell  230 ) to another one of the work cells  226  (e.g., the third work cell  232 ) using the overhead workpiece handler  166 . 
     In one or more examples, the method  1000  includes a step of (block  1002 ) holding the workpiece  102 . In one or more examples, the workpiece  102  is held using the workpiece holders  106 . For example, the workpiece  102  is held in one of the work cells  226  (e.g., the second work cell  230 ) using the workpiece holders  106 . In one or more examples, according to the method  1000 , the workpiece holders  106  hold the workpiece  102  in an upright or upstanding position such that the first surface  144  is oriented approximately vertical. 
     In one or more examples, the method  1000  includes a step of indexing the workpiece  102 . In one or more examples, the workpiece  102  is indexed using the workpiece holders  106 . 
     In one or more examples, the method  1000  includes a step of conforming the workpiece  102  to the desired shape of the workpiece  102 . In one or more examples, the workpiece  102  is conformed to the desired shape using the workpiece holders  106 . 
     In one or more examples, the method  1000  includes a step of digitizing at least a portion of the workpiece  102  with the workpiece  102  held in one of the work cells  226  (e.g., the second work cell  230 ), for example, in the indexed position and/or in the conformed shape as held by the workpiece holders  106 . In one or more examples, the step of digitizing at least a portion of the workpiece  102  includes a step of generating the measurement data  132  (e.g., real-time measurement data) for the workpiece  102 . In one or more examples, the measurement data  132  is generated using the metrology system  108 . In one or more examples, the measurement data  132  is generated while the workpiece  102  is held by the workpiece holders  106  in the indexed position and has the desired shape. In one or more examples, the step of digitizing at least a portion of the workpiece  102  includes a step of generating the real-time model  112  using the measurement data  132 . 
     In one or more examples, the method  1000  includes a step of comparing the real-time model  112  (e.g., real-time measurement data) to the as-built model  116  (e.g., as-built measurement data). In one or more examples, step of comparing the real-time model  112  to the as-built model  116  includes a step of determining a transform that fits the real-time model  112  to the as-built model  116 . 
     In one or more examples, the method  1000  includes a step of confirming that the workpiece  102  is appropriately indexed based on the comparison of the real-time model  112  to the as-built model  116 . In one or more examples, the method  1000  includes a step of confirming that the workpiece  102  is conformed to the as-built shape based on the comparison of the real-time model  112  to the as-built model  116 . 
     In one or more examples, the method  1000  includes a step of (block  1004 ) coupling the damping apparatus  174  to the workpiece  102 . In one or more examples, the damping apparatus  174  is coupled to the workpiece  102  between a directly adjacent pair of the workpiece holders  106 . In one or more examples, according to the method  1000 , the damping apparatus  174  is coupled to the first surface of the workpiece  102 . The damping apparatus  174  selectively controls the natural frequency  250  of the workpiece  102 , for example, prior to or during the machining operation performed using the machine tool  134 . 
     In one or more examples, the method  1000  includes a step of (block  1006 ) selectively controlling the natural frequency  250  of the workpiece  102 . In one or more examples, the natural frequency  250  of at least a portion (e.g., portion  254 ) of the workpiece  102  is performed using the damping apparatus  174 . 
     In one or more examples, according to the method  1000 , the step of (block  1006 ) controlling the natural frequency  250  of the workpiece  102  includes a step of (block  1008 ) modifying the natural frequency  250  of the workpiece  102 , such as of at least a portion (e.g., portion  254 ) of the workpiece  102 , for example, that extends between the directly adjacent pair of the workpiece holders  106 . For example, the natural frequency  250  of at least a portion (e.g., portion  254 ) of the workpiece  102  is modified by the damping apparatus  174  such that the modified natural frequency  252  of the workpiece  102  is less than a frequency of the machine-induced vibrations. 
     In one or more examples, the method  1000  includes a step of (block  1010 ) performing a machining operation on the workpiece  102 . Generally, damping apparatus  174  is coupled to the workpiece  102  (e.g., block  1004 ) and the natural frequency  250  of the workpiece  102  is selectively controlled or modified (e.g., block  1006 ) before the machining operation is performed on the workpiece  102  (e.g., block  1010 ). In one or more examples, the machining operation is performed while the workpiece  102  is held by the workpiece holders  106  and the damping apparatus  174  is coupled to the workpiece  102 . In one or more examples, the machining operation is automatically performed using the machine tool  134 , for example, under direction from the computing device  110 . 
     In one or more examples, the method  1000  includes a step of (block  1012 ) selectively controlling machine-induced vibrations in the workpiece  102  during the machining operation (e.g., vibrations induced by the machining operation). In one or more examples, the machine-induced vibrations are selectively controlled by controlling or modifying the natural frequency  250  of the workpiece  102  using the damping apparatus  174 . In one or more examples, step of (block  1012 ) selectively controlling the machine-induced vibrations includes a step of (block  1014 ) reducing the machine-induced vibrations in the workpiece  102  during the machining operation. 
     In one or more examples, according to the method  1000 , the step of (block  1006 ) selectively controlling the natural frequency  250  of the workpiece  102  includes a step of increasing the mass  103  of at least the portion  254  of the workpiece  102 . 
     In one or more examples, according to the method  1000 , the step of (block  1006 ) selectively controlling the natural frequency  250  of the workpiece  102  includes a step of increasing the stiffness  105  of at least the portion  254  of the workpiece  102 . 
     In one or more examples, according to the method  1000 , the natural frequency  250  of at least the portion  254  of the workpiece  102  is modified such that the modified natural frequency  252  of at least the portion  254  of the workpiece  102  is different than the frequency  260  of the oscillating force  256  applied to the workpiece  102  by the machine tool  134  during the machining operation. 
     Generally, a portion (e.g., portion  254 ) of the workpiece  102  for which the natural frequency  250  is being selectively controlled is a portion of the workpiece  102  upon which the machining operation is being performed. As illustrated in  FIGS.  4  and  5   , in one or more examples, the natural frequency  250  of the workpiece  102  is selectively controlled at more than one portion by coupling the plurality of damping apparatuses  104  to more than one portion  254  of the workpiece  102 . 
     In one or more examples, the natural frequency  250  of at least the portion  254  of the workpiece  102  maintained within a desired range during the machining operation. The desired range of the natural frequency  250  (e.g., the modified natural frequency  252 ) as selectively controlled by the damping apparatus  174  may depend on various factors, such as, but not limited to, the configuration (e.g., geometry, size, shape, material composition, etc.) of the workpiece  102 , the type of machining operation performed on the workpiece  102 , the type of machine tool  134  performing the machining operation, and the like. For example, in certain situations, for example, depending on the workpiece  102  and the machining operation being performed, some level of machine-induced vibration may be tolerable or desirable and in other situations little to no machine-induced vibration may be tolerable or desirable. As such, the desired range for the natural frequency  250  is selected and controlled by the damping apparatus  174 . 
     In one or more examples, according to the method  1000 , the natural frequency  250  of the portion  254  of the workpiece  102  is modified such that the modified natural frequency  252  of the portion  254  of the workpiece  102  is less than the frequency  260  of the oscillating force  256  applied to the workpiece  102  by the machine tool  134  during the machining operation. 
     In one or more examples, according to the method  1000 , the natural frequency  250  of the portion  254  of the workpiece  102  is modified such that the modified natural frequency  252  of the portion  254  of the workpiece  102  is less than approximately one-half of the frequency  260  of the oscillating force  256  applied to the workpiece  102  by the machine tool  134  during the machining operation. 
     In one or more examples, according to the method  1000 , the natural frequency  250  of the portion  254  of the workpiece  102  is modified such that the modified natural frequency  252  of the portion  254  of the workpiece  102  is less than approximately one-third of the frequency  260  of the oscillating force  256  applied to the workpiece  102  by the machine tool  134  during the machining operation. 
     In one or more examples, according to the method  1000 , the step of (block  1006 ) selectively controlling the natural frequency  250  of the workpiece  102  includes a step of selectively connecting one or more of the plurality of grippers  200  of the damping apparatus  174  to the workpiece  102  at one or more locations  222 . In one or more examples, the damping apparatus  174  includes the fixture base  198  and the plurality of grippers  200 , which is coupled to the fixture base  198 . Each one of the grippers  200  is selectively movable (e.g., extendable and retractable) relative to the fixture base  198  to be selectively connected to the workpiece  102 . The natural frequency  250  of the portion  254  of the workpiece  102  is modified by selecting one or more locations  222  on the portion of the workpiece  102  and selectively connecting one or more of the grippers  200  to the workpiece  102  at the one or more locations  222 . The select grippers  200  connected to the workpiece  102  at the locations  222  increase the mass  103  of at least a portion of the workpiece  102  and/or increase the stiffness  105  of at least a portion of the workpiece  102 . 
     In one or more examples, the method  1000  includes a step of (block  1016 ) determining the natural frequency  250  of the workpiece  102  or at least a portion (e.g., portion  254 ) of the workpiece  102 . The natural frequency  250  of the workpiece  102  can be determined by any one of various suitable techniques. In one or more examples, the natural frequency  250  is determined by analyzing the real-time model  112  of the workpiece  102 , for example, as held by the workpiece holders  106 , and calculating the natural frequency  250 . Alternatively, the natural frequency  250  can be measured. 
     Additionally, in one or more examples, the method  1000  includes a step of determining (e.g., detecting or measuring) a frequency of the machine-induced vibrations and/or the frequency  260  of the oscillating force  256  applied to the workpiece  102  by the machine tool  134  during the machining operation. 
     In one or more examples, the method  1000  includes a step of (block  1018 ) selecting the one or more locations  222  on the workpiece  102  for connection of the one or more of the plurality of grippers  200 . The one or more locations  222  are selected such that the modified natural frequency  252  of at least a portion (e.g., portion  254 ) of the workpiece  102  is less than the frequency  260  of the oscillating force  256  applied to the workpiece  102  by the machine tool  134  during the machining operation. In other words, the natural frequency  250  of at least a portion (e.g., portion  254 ) of the workpiece  102  is selectively controlled or modified by the select grippers  200  such that the modified natural frequency  252  of the workpiece  102  is less than a frequency of the machine-induced vibrations. 
     In one or more examples, the step of (block  1004 ) coupling the damping apparatus  174  to the workpiece  102  includes a step of extending the linear actuator  202  of at least one of a plurality of grippers  200  of the damping apparatus  174 . The step of (block  1004 ) coupling the damping apparatus  174  to the workpiece  102  also includes a step of placing the vacuum cup  204 , coupled to the linear actuator  202 , in contact with the workpiece  102 . The step of (block  1004 ) coupling the damping apparatus  174  to the workpiece  102  further includes a step of applying vacuum between the vacuum cup  204  and the workpiece  102 . 
     In one or more examples, the step of (block  1004 ) coupling the damping apparatus  174  to the workpiece  102  also includes a step of engaging the power-transmitting component  212  of at least the one of the plurality of grippers  200  to extend the linear actuator  202  from the first position  268  to the second position  270  that places the vacuum cup  204  in contact with the workpiece  102 . Upon contact of vacuum cup  204  with the workpiece  102 , the step of (block  1004 ) coupling the damping apparatus  174  to the workpiece  102  also includes a step of disengaging the power-transmitting component  212  to enable free extension of the linear actuator  202 . With the vacuum cup  204  in contact with the workpiece  102  and the power-transmitting component  212  disengaged, the step of (block  1004 ) coupling the damping apparatus  174  to the workpiece  102  further includes a step of further extending the linear actuator  202  to a third position  272  in response to the step of applying the vacuum between the vacuum cup  204  and the workpiece  102 . With the vacuum formed between the vacuum cup  204  and the workpiece  102  and the power-transmitting component  212  disengaged, the step of (block  1004 ) coupling the damping apparatus  174  to the workpiece  102  additionally includes a step of engaging the actuator stop-lock  210  of at least the one of the plurality of grippers  200  to lock the linear actuator  202  in the third position  272 . 
     In one or more examples, according to the method  1000 , each one of the grippers  200  includes the linear actuator  202 , the vacuum cup  204  that is coupled to the linear actuator  202 , and the actuator control unit  208  that controls extension and retraction of the linear actuator  202 . In one or more examples, according to the method  1000 , each one of the grippers  200  includes the power-transmitting component  212  that drives extension and retraction of the linear actuator  202  and the actuator stop-lock  210  that selectively locks a position of the linear actuator  202 . 
     In one or more examples, the method  1000  includes a step of detecting contact of the vacuum cup  204  with the workpiece  102 . In one or more examples, the step of detecting contact is performed using the sensor  206 . 
     In one or more examples, according to the method  1000 , the fixture base  198  includes the pedestal  216  and the stanchion  218  that is coupled to the pedestal  216 . The grippers  200  are coupled to the stanchion  218 . In one or more examples, the step of (block  1004 ) coupling the damping apparatus  174  to the workpiece  102  includes a step of moving the pedestal  216  relative to the workpiece  102 . In one or more examples, the step of (block  1004 ) coupling the damping apparatus  174  to the workpiece  102  includes a step of moving the stanchion  218  relative to the pedestal  216 . In one or more examples, the step of (block  1004 ) coupling the damping apparatus  174  to the workpiece  102  includes a step of extending one or more of the grippers  200  from the stanchion  218 . 
     In one or more examples, the method  1000  includes a step of digitizing at least a portion of the workpiece  102  after the machining operation (e.g., block  1006 ). In one or more examples, the step of digitizing at least a portion of the workpiece  102  includes a step of generating the measurement data  132  (e.g., as-machined measurement data) for the workpiece  102 . In one or more examples, the measurement data  132  is generated using the metrology system  108 . In one or more examples, the measurement data  132  is generated while the workpiece  102  is held by the workpiece holders  106  and has the desired shape. In one or more examples, the step of digitizing at least a portion of the workpiece  102  includes a step of generating the as-machined model  180  using the measurement data  132 . 
     In one or more examples, at least a portion of the steps described above are repeated a number of times as the workpiece  102  moves through the work cells  226  and a number of post-processing operations are performed on the workpiece  102 . 
     The present disclosure is also directed to a system (e.g., the system  100 ) for damping vibrations in the workpiece  102  implemented according to the method  1000 . The present disclosure is further directed to the workpiece  102  manufacturing according to the method  1000 . The present disclosure is further directed to a portion of the aircraft  1200  assembled according to the method  1000 . 
     Referring generally to  FIGS.  1 - 12    and particularly to  FIG.  14   , by way of examples, the present disclosure is also directed to a method  2000  for selectively increasing the mass  103  of the workpiece  102 . In one or more examples, the method  2000  is implemented during, or forms a portion of, a method for processing or manufacturing the workpiece  102 . In one or more examples, the method  2000  is implemented during, or forms a portion of, a method for fabricating a portion of an aircraft  1200  (e.g., as shown in  FIG.  17   ). In one or more examples, the method  2000  is implemented using the system  100 . In one or more examples, the method  2000  is implemented using the damping apparatus  174 . 
     In one or more examples, the method  2000  includes a step of (block  2002 ) selecting one or more locations  222  on the workpiece  102 . In one or more examples, the method  2000  also includes a step of (block  2004 ) coupling the damping apparatus  174  the workpiece  102  at the one or more locations  222 . In one or more examples, the method  2000  further includes a step of (block  2006 ) increasing the mass  103  of at least a portion (e.g., portion  254 ) of the workpiece  102 , including the one or more locations  222 , by the mass  107  of the damping apparatus  174 . 
     In one or more examples, the step of (block  2004 ) coupling the damping apparatus  174  to the workpiece  102  includes a step of coupling one or more of the plurality of grippers  200  of the damping apparatus  174  to a surface (e.g., first surface  144 ) of the workpiece  102  at the one or more locations  222 . 
     In one or more examples, the method  2000  is an example of the step of (block  1006 ) selectively controlling the natural frequency  250  of the workpiece  102  of the method  1000  (e.g., as shown in  FIG.  13   ). Accordingly, while not explicitly illustrated in  FIG.  14   , the method  2000  may also include one or more of the operational steps described herein above and/or illustrated in  FIG.  13    in reference to the method  1000 . 
     In one or more examples, according to the method  2000 , the workpiece  102  is made of a composite material. In one or more examples, according to the method  2000 , the workpiece  102  is made of a metallic material. 
     Referring generally to  FIGS.  1 - 12    and particularly to  FIG.  15   , by way of examples, the present disclosure is also directed to a method  3000  for selectively modifying the natural frequency  250  of the workpiece  102 . In one or more examples, the method  3000  is implemented during, or forms a portion of, a method for processing or manufacturing the workpiece  102 . In one or more examples, the method  3000  is implemented during, or forms a portion of, a method for fabricating a portion of an aircraft  1200  (e.g., as shown in  FIG.  17   ). In one or more examples, the method  3000  is implemented using the system  100 . In one or more examples, the method  3000  is implemented using the damping apparatus  174 . 
     In one or more examples, the method  3000  includes a step of (block  3002 ) determining the natural frequency  250  of the workpiece  102 . In one or more examples, the method  3000  includes a step of (block  3004 ) modifying the natural frequency  250  of at least a portion (e.g., portion  254 ) of the workpiece  102  by at least one of a step of (block  3006 ) increasing a mass  103  of at least the portion  254  of the workpiece  102  and/or a step of (block  3008 ) increasing a stiffness  105  of at least a portion  254  of the workpiece  102  when the oscillating force  256  is applied to the workpiece  102  by the machine tool  134  during the machining operation. 
     In one or more examples, the natural frequency  250  is modified, for example, the mass  103  and/or the stiffness  105  of the workpiece  102  is increased, such that the modified natural frequency  252  of at least the portion  254  of the workpiece  102  is less than the frequency  260  of the oscillating force  256  applied to the workpiece  102  by the machine tool  134  during the machining operation. 
     In one or more examples, the method  3000  is an example of the step of (block  1008 ) modifying the natural frequency  250  of the workpiece  102  and the step of (block  1016 ) determining the natural frequency  250  of the workpiece  102  of the method  1000  (e.g., as shown in  FIG.  13   ). Accordingly, while not explicitly illustrated in  FIG.  15   , the method  3000  may also include one or more of the operational steps described herein above and/or illustrated in  FIG.  13    in reference to the method  1000 . 
     In one or more examples, according to the method  3000 , the workpiece  102  is made of a composite material. In one or more examples, according to the method  3000 , the workpiece  102  is made of a metallic material. 
     Referring now to  FIGS.  16  and  17   , examples of the system  100 , the method  1000 , and the workpiece  102  may be related to, or used in the context of, an aircraft manufacturing and service method  1100 , as shown in the flow diagram of  FIG.  16    and the aircraft  1200 , as schematically illustrated in  FIG.  17   . For example, the aircraft  1200  and/or the aircraft production and service method  1100  may utilize the workpiece  102  that is held and machined while damping machine-induced vibration using the system  100 , described herein and illustrated in  FIGS.  1 - 12   , and/or according to the method  1000 , described herein and illustrated in  FIG.  13   , the method  2000 , described herein and illustrated in  FIG.  14    and/or the method  3000 , described herein and illustrated in  FIG.  15   . 
     Referring to  FIG.  17   , examples of the aircraft  1200  may include an airframe  1202  having the interior  1206 . The aircraft  1200  also includes a plurality of high-level systems  1204 . Examples of the high-level systems  1204  include one or more of a propulsion system  1208 , an electrical system  1210 , a hydraulic system  1212 , an environmental system  1214  and a flight control system  1216 . In other examples, the aircraft  1200  may include any number of other types of systems, such as a communications system, a flight control system, a guidance system, a weapons system, and the like. In one or more examples, the workpiece  102  made (e.g., held, machined and/or processed) using the system  100  and/or according to the method  1000  forms a component of the airframe  1202 , such as a wing  1220 , a fuselage  1218 , a tail  1224 , a vertical stabilizer  1226 , a horizontal stabilizer  1228  or a panel, a stringer, a spar, or another component thereof. 
     Referring to  FIG.  16   , during pre-production, the service method  1100  includes specification and design of the aircraft  1200  (block  1102 ) and material procurement (block  1104 ). During production of the aircraft  1200 , component and subassembly manufacturing (block  1106 ) and system integration (block  1108 ) of the aircraft  1200  take place. Thereafter, the aircraft  1200  goes through certification and delivery (block  1110 ) to be placed in service (block  1112 ). Routine maintenance and service (block  1114 ) includes modification, reconfiguration, refurbishment, etc. of one or more systems of the aircraft  1200 . 
     Each of the processes of the service method  1100  illustrated in  FIG.  16    may be performed or carried out by a system integrator, a third party, and/or an operator (e.g., a customer). For the purposes of this description, a system integrator may include, without limitation, any number of spacecraft manufacturers and major-system subcontractors; a third party may include, without limitation, any number of vendors, subcontractors, and suppliers; and an operator may be an airline, leasing company, military entity, service organization, and so on. 
     Examples of the system  100 , the damping apparatus  174  and the methods  1000 ,  2000 ,  3000  shown and described herein may be employed during any one or more of the stages of the manufacturing and service method  1100  shown in the flow diagram illustrated by  FIG.  16   . In an example, manufacture of the workpiece  102  in accordance with the methods  1000 ,  2000 ,  3000  and/or using the system  100  or the damping apparatus  174  may form a portion of component and subassembly manufacturing (block  1106 ) and/or system integration (block  1108 ). Further, the workpiece  102  manufactured in accordance with the methods  1000 ,  2000 ,  3000  and/or using the system  100  or the damping apparatus  174  may be utilized in a manner similar to components or subassemblies prepared while the aircraft  1200  is in service (block  1112 ). Also, the workpiece  102  manufactured in accordance with the methods  1000 ,  2000 ,  3000  and/or using the system  100  or the damping apparatus  174  may be utilized during system integration (block  1108 ) and certification and delivery (block  1110 ). Similarly, manufacture of the workpiece  102  in accordance with the methods  1000 ,  2000 ,  3000  and/or using the system  100  or the damping apparatus  174  may be utilized, for example and without limitation, while the aircraft  1200  is in service (block  1112 ) and during maintenance and service (block  1114 ). For example, spare and or replacement composite parts may be fabricated in accordance with the methods  1000 ,  2000 ,  3000  and/or using the system  100  or the damping apparatus  174 , which may be installed due to a prescribed maintenance cycle or after a realization of damage to a composite part. 
     In can be appreciated that performing at least a portion of the processing operation on the workpiece  102  while the workpiece  102  is held, indexed and/or conformed to the desired shape by the workpiece holders  106  and while machine-induced vibration is dampened using the damping apparatus  174  in one or more of the work cells  226 , may improve the accuracy and speed of the processing operation. Furthermore, updating the model of the workpiece  102  (e.g., the as-machined model  180 ) after each subsequent processing operation may enable determinant assembly or predictive assembly using the workpiece  102 . 
     Although an aerospace example is shown, the examples and principles disclosed herein may be applied to other industries, such as the automotive industry, the space industry, the construction industry, and other design and manufacturing industries. Accordingly, in addition to aircraft, the examples and principles disclosed herein may apply to composite structures, systems, and methods of making the same for other types of vehicles (e.g., land vehicles, marine vehicles, space vehicles, etc.) and stand-alone structures. 
     The preceding detailed description refers to the accompanying drawings, which illustrate specific examples described by the present disclosure. Other examples having different structures and operations do not depart from the scope of the present disclosure. Like reference numerals may refer to the same feature, element, or component in the different drawings. Throughout the present disclosure, any one of a plurality of items may be referred to individually as the item and a plurality of items may be referred to collectively as the items and may be referred to with like reference numerals. Moreover, as used herein, a feature, element, component or step preceded with the word “a” or “an” should be understood as not excluding a plurality of features, elements, components or steps, unless such exclusion is explicitly recited. 
     Illustrative, non-exhaustive examples, which may be, but are not necessarily, claimed, of the subject matter according to the present disclosure are provided above. Reference herein to “example” means that one or more feature, structure, element, component, characteristic, and/or operational step described in connection with the example is included in at least one aspect, embodiment, and/or implementation of the subject matter according to the present disclosure. Thus, the phrases “an example,” “another example,” “one or more examples,” and similar language throughout the present disclosure may, but do not necessarily, refer to the same example. Further, the subject matter characterizing any one example may, but does not necessarily, include the subject matter characterizing any other example. Moreover, the subject matter characterizing any one example may be, but is not necessarily, combined with the subject matter characterizing any other example. 
     As used herein, a system, apparatus, device, structure, article, element, component, or hardware “configured to” perform a specified function is indeed capable of performing the specified function without any alteration, rather than merely having potential to perform the specified function after further modification. In other words, the system, apparatus, device, structure, article, element, component, or hardware “configured to” perform a specified function is specifically selected, created, implemented, utilized, programmed, and/or designed for the purpose of performing the specified function. As used herein, “configured to” denotes existing characteristics of a system, apparatus, structure, article, element, component, or hardware that enable the system, apparatus, structure, article, element, component, or hardware to perform the specified function without further modification. For purposes of this disclosure, a system, apparatus, device, structure, article, element, component, or hardware described as being “configured to” perform a particular function may additionally or alternatively be described as being “adapted to” and/or as being “operative to” perform that function. 
     Unless otherwise indicated, the terms “first,” “second,” “third,” etc. are used herein merely as labels, and are not intended to impose ordinal, positional, or hierarchical requirements on the items to which these terms refer. Moreover, reference to, e.g., a “second” item does not require or preclude the existence of, e.g., a “first” or lower-numbered item, and/or, e.g., a “third” or higher-numbered item. 
     For the purpose of this disclosure, the terms “coupled,” “coupling,” and similar terms refer to two or more elements that are joined, linked, fastened, attached, connected, put in communication, or otherwise associated (e.g., mechanically, electrically, fluidly, optically, electromagnetically) with one another. In various examples, the elements may be associated directly or indirectly. As an example, element A may be directly associated with element B. As another example, element A may be indirectly associated with element B, for example, via another element C. It will be understood that not all associations among the various disclosed elements are necessarily represented. Accordingly, couplings other than those depicted in the figures may also exist. 
     For the purpose of the present disclosure, the term “position” of an item refers to a location of the item in three-dimensional space relative to a fixed reference frame and an angular orientation of the item in three-dimensional space relative to the fixed reference frame. 
     As used herein, relative positional (e.g., locational and/or orientational) terms, such as parallel, perpendicular, horizontal, vertical, and similar terms include approximations of such positional terms (e.g., approximately parallel, approximately perpendicular, approximately, vertical, approximately horizontal, etc.). 
     As used herein, the term “approximately” refers to or represent a condition that is close to, but not exactly, the stated condition that still performs the desired function or achieves the desired result. As an example, the term “approximately” refers to a condition that is within an acceptable predetermined tolerance or accuracy, such as to a condition that is within  10 % of the stated condition. However, the term “approximately” does not exclude a condition that is exactly the stated condition. As used herein, the term “substantially” refers to a condition that is essentially the stated condition that performs the desired function or achieves the desired result. 
     Conditional language such as, among others, “can” or “may,” unless specifically stated otherwise, are understood within the context as used to generally convey that a certain example includes, while other examples do not include, certain features, elements and/or steps. Thus, such conditional language is not generally intended to imply that features, elements and/or steps are in any way required for one or more examples or that one or more examples necessarily include logic for deciding, with or without user input or prompting, whether these features, elements and/or steps are included or are to be performed in any example. 
       FIGS.  1 - 12  and  17   , referred to above, may represent functional elements, features, or components thereof and do not necessarily imply any particular structure. Accordingly, modifications, additions and/or omissions may be made to the illustrated structure. Additionally, those skilled in the art will appreciate that not all elements, features, and/or components described and illustrated in  FIGS.  1 - 12  and  17   , referred to above, need be included in every example and not all elements, features, and/or components described herein are necessarily depicted in each illustrative example. Accordingly, some of the elements, features, and/or components described and illustrated in  FIGS.  1 - 12  and  17    may be combined in various ways without the need to include other features described and illustrated in  FIGS.  1 - 12  and  17   , other drawing figures, and/or the accompanying disclosure, even though such combination or combinations are not explicitly illustrated herein. Similarly, additional features not limited to the examples presented, may be combined with some or all of the features shown and described herein. Unless otherwise explicitly stated, the schematic illustrations of the examples depicted in  FIGS.  1 - 12  and  17   , referred to above, are not meant to imply structural limitations with respect to the illustrative example. Rather, although one illustrative structure is indicated, it is to be understood that the structure may be modified when appropriate. Accordingly, modifications, additions and/or omissions may be made to the illustrated structure. Furthermore, elements, features, and/or components that serve a similar, or at least substantially similar, purpose are labeled with like numbers in each of  FIGS.  1 - 12  and  17   , and such elements, features, and/or components may not be discussed in detail herein with reference to each of  FIGS.  1 - 12  and  17   . Similarly, all elements, features, and/or components may not be labeled in each of  FIGS.  1 - 12  and  17   , but reference numerals associated therewith may be utilized herein for consistency. 
     In  FIGS.  13 - 15   , referred to above, the blocks may represent operations, steps, and/or portions thereof and lines connecting the various blocks do not imply any particular order or dependency of the operations or portions thereof. It will be understood that not all dependencies among the various disclosed operations are necessarily represented.  FIGS.  13 - 15    and the accompanying disclosure describing the operations of the disclosed methods set forth herein should not be interpreted as necessarily determining a sequence in which the operations are to be performed. Rather, although one illustrative order is indicated, it is to be understood that the sequence of the operations may be modified when appropriate. Accordingly, modifications, additions and/or omissions may be made to the operations illustrated and certain operations may be performed in a different order or simultaneously. Additionally, those skilled in the art will appreciate that not all operations described need be performed. 
     Further, references throughout the present specification to features, advantages, or similar language used herein do not imply that all of the features and advantages that may be realized with the examples disclosed herein should be, or are in, any single example. Rather, language referring to the features and advantages is understood to mean that a specific feature, advantage, or characteristic described in connection with an example is included in at least one example. Thus, discussion of features, advantages, and similar language used throughout the present disclosure may, but do not necessarily, refer to the same example. 
     The described features, advantages, and characteristics of one example may be combined in any suitable manner in one or more other examples. One skilled in the relevant art will recognize that the examples described herein may be practiced without one or more of the specific features or advantages of a particular example. In other instances, additional features and advantages may be recognized in certain examples that may not be present in all examples. Furthermore, although various examples of the system  100 , the damping apparatus  174 , the methods  1000 ,  2000 ,  3000  and the workpiece  102  have been shown and described, modifications may occur to those skilled in the art upon reading the specification. The present application includes such modifications and is limited only by the scope of the claims.