Abstract:
The invention discloses an improved method and apparatus to statically equalize the span wise and chord wise moments of a detached plurality of radial projections. These detached radial projections are associated with a rotating assembly and constitute the majority of its rotating mass. When installed on the rotating assembly, the balanced radial projections will necessarily produce a center of rotating mass approximately concentric with its axis of rotation, thereby minimizing vibrations associated with its rotation. The method to statically equalize the span wise moments of the radial projections comprises first determining the span wise moment by finding the center of gravity and multiplying the distance from the center of gravity to the plane of attachment of the radial projection to the rotating assembly by its total weight.

Description:
CROSS REFERENCE TO RELATED APPLICATIONS 
     Not applicable. 
     STATEMENT REGARDING FEDERALLY SPONSORED RESEARCH AND DEVELOPMENT 
     Not applicable 
     BACKGROUND OF INVENTION 
     1. Field of Invention 
     This invention relates to the balancing of a rotating assembly having radial projections such that the vibratory effect of having the center of rotating mass eccentric to the axis of rotation is minimized. 
     2. Related Art 
     Whether used for aerodynamic lift, for the generation of power, or for cooling, the radial projections, or air foils in these cases, are part of a rotating assembly. It is necessary that the center of mass of the rotating assembles is concentric with its axis of rotation for optimal performance of these respective functions. Any deviation from this concentricity will represent additional forces which must be borne by a given structure that supports the rotating assembly. These additional forces manifest themselves as vibration and can not only interfere or diminish the ability of the rotating object to perform its function but can also accelerate the fatigue life of all the interconnected components themselves e.g. bearings, gears, shafts, structural supports connected to the rotating assembly. In wind or water turbines, increasing the degree of unbalance not only decreases the mechanical life of connected components but will also increase the necessary wind or water velocity required to for the generation of power. 
     Investigation into related art shows several methods to statically balance detached blades. Referenced in U.S. Pat. No. 5,824,897 to Beachum et al. (1998) and taught in U.S. Pat. No. 4,991,437 to Hanchett (1991) is a method to have a specimen blade connected to a reference blade over a fixed fulcrum where the fulcrum is positioned at the point of connection between the two blades. Corrective weight is either added or subtracted in a trial and error method until the respective blades are in equilibrium with each other. That is to say, if the blades are positioned in a horizontal fashion and released, the blades will remain stationary or balanced. The size of the fulcrum assembly would be proportional to the size of the blade being balanced. On large wind turbine blades whose length can be in excess of 60 meters and whose weight can be in excess of 16,000 kg, the fixture size would render it non-portable. Additionally, the area to balance the blades would be in excess of twice the blade length. Furthermore, a trial and error method is less efficient with respect to time as compared with having a prescriptive weight and distance correction. It would be impractical to establish a profile of weight distribution or span wise and chord wise moments for a radial projection. The method and apparatus does not lend itself to any type of automation. 
     U.S. Pat. No. 5,824,897 to Beachum et al. (1998) discloses a fixture where a single blade is attached to the fixture at its point of attachment and multiple load cells are used to indicate weight. The moment of the blade is then calculated based on the measurement indication of the load cells and the relative distances to the point of attachment. Corrective weight then can be added or subtracted based upon a virtual master blade specification. The fixture is limited to the application of helicopter blades which are of relatively short length as compared to a blade of a wind turbine whose length may exceed 60 meters. Multiple fixtures would be required to service blades from multiple applications. The fixture would necessarily be proportionate to the size of the blade being balanced, rendering the fixture to be non-portable and subsequently not suitable for field use in the extreme case of blades associated with wind turbines. Additionally, it would be impractical to establish a profile of weight distribution or span wise and chord wise moments for a radial projection. The method and apparatus does not lend itself to any type of automation. 
     It is well known in the art to balance a rotating mass with radial projections as a complete assembly. The art is generally limited to rotating masses which are sufficiently small in diameter, have sufficient speed, and can be performed without external forces such as those which are environmentally induced. U.S. Pat. No. 5,140,856 to Larson (1992) teaches one method of a balancing a complete assembly whose parameters fall outside of the well known art which requires the use of fixtures, specialized equipment and associated skill set, and requires personnel to perform the process at great heights and in proximity to rotating equipment. The method is time consuming and also extremely subject to environmental influences such as wind which will thereby affect the accuracy of the results. 
     U.S. Pat. No. 7,370,529 to Lenz (2008) discloses a method of balancing a rotating object with radial projections as a complete assembly but is limited to objects where the radial projections rotate around a stationary center. This method only covers a limited class of objects and certainly does not include the class of objects associated with helicopters and wind turbines. 
     It is desirable to have an improved method and apparatus to balance radial projections that provides a simple, practical, portable, prescriptive, and economical means which not only encompasses the class of radial projections addressed in prior art but is also not restricted to the length of the radial projection as in the extreme case of wind turbine blades. It is also desirable to have a method and apparatus which can allow minimal human intervention during the process as can be realize through process automation. 
     BRIEF SUMMARY OF INVENTION 
     One object of the invention is to provide a method and apparatus which can not only be used to balance radial projections detached from a rotating assembly but to balance those radial projections whose lengths and weights are extreme as in the case of the wind turbine application and to balance them relative to the radial projections attached to a given rotating assembly. 
     It is another object of the invention to provide an apparatus which is simple and portable for the all lengths of radial projections. 
     It is yet another object of the invention to provide a method and apparatus to establish a profile of weight distributions and associated span wise and chord wise moments of a radial projection for comparison to a reference profile, to balance a radial projection, and to be suitable for process automation. 
    
    
     
       BRIEF DESCRIPTION OF DRAWINGS 
         FIG. 1  illustrates the free body force diagram of a radial projection in horizontal equilibrium. 
         FIG. 2  illustrates an isometric view of a preferred embodiment having moveable fulcrum assembly supported from beneath the radial projection with planar target as the objective of the laser. 
         FIG. 2A  illustrates a distal end view of  FIG. 2 . 
         FIG. 2B  illustrates an isometric view of the moveable fulcrum assembly. 
         FIG. 2C  illustrates a magnified view of one end of the moveable fulcrum assembly. 
         FIG. 3  illustrates an isometric view of another preferred embodiment having the moveable fulcrum assembly supported from above the radial projection with planar target as the objective of the laser. 
         FIG. 3A  illustrates a distal end view of  FIG. 3  without planar target, for clarity. 
         FIG. 4  illustrates an isometric view of the fulcrum assembly. 
         FIG. 4A  illustrates an exploded part view of one end of fulcrum assembly with fulcrum wheel omitted from illustration. 
         FIG. 4B  illustrates the fulcrum and fulcrum axle with anti-friction bearing. 
         FIG. 5  illustrates an isometric view of another preferred embodiment where a lower supported, moveable fulcrum assembly is used with a perpendicularly bi-axial fulcrum and the planar target as the objective of the laser. 
         FIG. 6  illustrates an isometric view of the perpendicularly bi-axial fulcrum with adjustable height. 
         FIG. 6A  illustrates a side view of perpendicularly bi-axial fulcrum with adjustable height. 
       
         
           
                 
               
                 
                 
               
             
                 
                     
                 
                 
                   Reference Numerals In Drawings 
                 
                 
                     
                 
               
               
                 
                     
                 
               
            
             
                 
                   20 
                   Radial Projection e.g. wind turbine blade 
                 
                 
                   21 
                   Target Support 
                 
                 
                   22 
                   Moveable Fulcrum Assembly 
                 
                 
                   23 
                   Planar Target 
                 
                 
                   24 
                   Laser 
                 
                 
                   26 
                   Crane Load Cell 
                 
                 
                   28 
                   Arm Load Cell 
                 
                 
                   30 
                   Lower Fulcrum Support Assembly 
                 
                 
                   32 
                   Fulcrum 
                 
                 
                   34 
                   Guide Pin 
                 
                 
                   36 
                   Lower Support Load Cell 
                 
                 
                   38 
                   Fulcrum Axle 
                 
                 
                   40 
                   Anti-Friction Bearing 
                 
                 
                   44 
                   Hoist Separator Plate 
                 
                 
                   46 
                   Fulcrum Wheel 
                 
                 
                   48 
                   Upper Fulcrum Support 
                 
                 
                   50 
                   Fulcrum Anti-Friction Bearing 
                 
                 
                   52 
                   Reversible Fulcrum Clamping Spacer 
                 
                 
                   54 
                   Outside Clamping Spacer 
                 
                 
                   56 
                   Upper Fulcrum Support Anti-Friction Bearing 
                 
                 
                   58 
                   Perpendicularly Bi-Axial Fulcrum 
                 
                 
                   60 
                   Hydraulic Cylinder 
                 
                 
                   64 
                   Hydraulic Ram 
                 
                 
                   62 
                   Axial Attachment Plate 
                 
                 
                   66 
                   Bi-Axial Anti-Friction Bearings 
                 
                 
                   68 
                   Pressure Transducer 
                 
                 
                     
                 
               
            
           
         
       
     
    
    
     Before the embodiments of the invention are explained in detail, it is to be understood that the invention is not limited in its application to the details of construction and the arrangements of the components set forth in the following description or illustrated in the drawings. The invention is capable of other embodiments and of being practiced or being carried out in various ways. Also, it is understood that the phraseology and terminology used herein are for the purpose of description and should not be regarded as limiting. The use of “including” and “comprising” and variations thereof herein is meant to encompass the items listed thereafter and the equivalents thereof. The use of “consisting of” and variations thereof herein is meant to encompass only the items listed thereafter and equivalents thereof. 
     DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS 
     Description— FIG. 1   
     In order to appreciate the method and apparatus disclosed, one must first understand basis upon which the objects of the invention can be realized.  FIG. 1  is a free body equilibrium force diagram which illustrates the forces due to the distributed weight of a radial projection  20 , the centers of gravity at which these distributed weights can be said to act, and the reaction force due to a moveable fulcrum assembly  22 . In equilibrium, the sum of the moments around any point must be necessarily zero. In this case, a moment is the force of weight due to gravity multiplied by the perpendicular distance to moveable fulcrum assembly  22 . It is given that there will be a distributed weight W A  located at a center of gravity Cg A  of radial projection  20  to the left of moveable fulcrum assembly  22 . It is also given that there will be a distributed weight W B  located at a center of gravity Cg B  to the right of moveable fulcrum assembly  22 . Summing the moments around moveable fulcrum assembly  22 , it follows that:
 
ΣM CgRP =0
 
 M   A   =L   A   ×W   A  
 
 M   B   =L   B   ×W   B  
 
 M   A   −M   B =0
 
M A =M B  
 
 L   A   ×W   A   =L   B   ×W   B  
 
 L   A   /L   B   =W   B   /W   A  
 
     Since the center of gravity of radial projection  20  is unknown, one can find it by adjusting moveable fulcrum assembly  22  along radial projection  20 . When radial projection  20  no longer has the tendency rotate from a substantially horizontal position; the state of equilibrium has been reached; the sum of the moments around moveable fulcrum assembly  22  are zero; and the center of gravity of radial projection  20  has thus been determined. Once the location of the center of gravity of radial projection  20  has been determined, the span wise moment of radial projection  20  can be calculated by applying the total weight of radial projection  20  at the location of its center of gravity and multiplying the distance from its center of gravity to the plane of attachment of radial projection  20  by the total weight.
 
Span Moment= W   RP   ×L   POA  
 
     If all of the span wise moments of the radial projections associated with a rotating assembly are equal, it necessarily follows that center of rotating mass of the assembly will be concentric with its axis of rotation. 
     It can be appreciated through the same process there can be a moment around a longitudinal axis parallel to the span of radial projection  20  where centers of gravity would exist on an axis perpendicular the span called the chord wise axis. It is then given that a chord wise moment can exist around any arbitrary axis parallel to the span wise axis and contained within radial projection  20 . This arbitrary axis could be equivalent to the axis around which radial projection  20  adjusts for pitch. For each radial projection to behave in a similar fashion during operation the chord wise moments of each radial projection should be equal or they will produce a dynamic imbalance of the rotating assembly. The following details of the preferred embodiments are explained with this above background information in mind. 
     Description— FIGS. 2 ,  2 A,  2 B,  2 C Preferred Embodiment 
       FIG. 2  illustrates an isometric view of moveable fulcrum assembly  22  supported by a lower fulcrum support assembly  30  from beneath radial projection  20 . The proper relationship between moveable fulcrum assembly  22  and lower fulcrum support assembly  30  is established with a guide pin  34  shown in  FIG. 2C . The guide pins  34  are fixed in fulcrum support assembly  30 . Guide pins  34  are received by an upper fulcrum support  48 . 
     The moveable fulcrum assembly  22  is adjusted along the span wise direction of radial projection  20  until a substantially horizontal equilibrium is established. It should be appreciated that the translation of moveable fulcrum assembly  22  can be accomplished in a variety of manners e.g. applying linear torque to lower fulcrum support assembly  30  with a winch or hoist or having lower fulcrum support assembly  30  powered by an electric or hydraulic motor. The lower fulcrum support assembly  30  could be modified such that it is necessarily guided by a track to assure its relational movement to radial projection  20 . 
     Once this equilibrium state is realized, the distance is measured from a laser  24  mounted on the plane of attachment of radial projection  20  to a planar target  23 , which is now coincident with its center of gravity and the rotational axis of a fulcrum  32 . In this state of equilibrium, the total weight is also measured by summing the forces at a lower support load cell  36  located at opposite ends of moveable fulcrum assembly  22  between upper fulcrum support  48  and lower fulcrum support assembly  30 . Furthermore, a predetermined distance has been established in the positioning of the chord wise direction of radial projection  20  along the rotational axis of fulcrum  32  from a preferred longitudinal axis on radial projection  20  to each of the load cell locations. 
     The measurements of force and distance are communicated to a conventional computer common in the art of process measurement where the span wise moment is calculated according to the sum of lower support load cell  36  measurements which are biased to a zero force when moveable fulcrum assembly  22  is empty of radial projection  20 . With the predetermined distance of the preferred longitudinal axis to each of lower support load cell  36 , respectively, the chord wise moment is calculated. The measurements and calculations are displayed on terminal and stored to storage media. Once the process has been completed for all radial projections of a rotating assembly, a preferred span moment is chosen by to which all of the other radial projections will be adjusted. Practically, the maximum span moment of the radial projections is chosen as the preferred span moment as it is easier to add weight to the other radial projections than it is to remove it. Additionally, a preferred chord wise moment is chosen as the maximum chord wise moment of the radial projections for the same reason. 
     It should be appreciated that the communication between laser  24  and lower support load cell  36  can be achieved by either a wired or wireless technology as are both common in the measurement and process control art. It should also be appreciated that all measurements can be displayed numerically, graphically, or both as is common in the measurement and process control arts. It should be further appreciated that any data obtained can be stored and retrieved by any means common in the art of data processing. 
     It is desirable to add a minimum amount of weight to correct both the span wise moment and cord wise moment to the preferred span wise and preferred chord wise moment. For each radial projection, the corrective weight necessary to obtain the preferred chord wise moment is subtracted from the corrective weight necessary to obtain the preferred span wise moment. The resulting corrective span wise weight is then placed at a distance off of the preferred longitudinal axis such that the product of the resulting corrective span weight and the chord wise off axis distance equals the preferred cord wise moment. Simultaneously, the longitudinal placement of the resulting corrective weight will result in the preferred span moment. 
     Description— FIGS. 3 ,  3 A,  4 ,  4 B Preferred Embodiment 
       FIG. 3  illustrates an isometric view of another preferred embodiment.  FIG. 3A  illustrates a distal end view where moveable fulcrum assembly  22  supported by upper fulcrum support  48  from above radial projection  20 . The moveable fulcrum assembly  22  is adjusted along the span wise direction of radial projection  20  until a substantially horizontal equilibrium is established. In this configuration, the distal end of radial projection  20  can be placed on fulcrum  32 , and translation of moveable fulcrum assembly  22  can be achieved by applying a hoist or crane to a crane load cell  26  and pulling it in the intended direction of travel by hoisting at an acute angle to radial projection  20  until a horizontal state of equilibrium is established. 
       FIG. 4  illustrates moveable fulcrum assembly  22 . It illustrates fulcrum  32 , a fulcrum axle  38 , a fulcrum wheel  46 , and upper fulcrum support  48 .  FIG. 4A  illustrates an exploded view of one end of moveable fulcrum assembly  22  with the fulcrum wheel  46  removed for clarity. In this arrangement, fulcrum  32  is supported by the fulcrum axle  38  with a fulcrum anti-friction bearing  50  which allows the rotation of fulcrum  32  relative to the fulcrum axle  38 . If a mode of operation is to have fulcrum  32  rotate in synchronicity with the fulcrum wheel  46 , the arrangement as illustrated achieves the mode by clamping the inner race of a upper fulcrum support anti-friction bearing  56  to an outside clamping spacer  54 , to the fulcrum wheel  46 , not shown, to a reversible fulcrum clamping spacer  52 , and to fulcrum  32 . This mode of operation is desirable if moveable fulcrum assembly  22  is support by lower support assembly  30  and small adjustments to the longitudinal position of radial projection  20  are necessary to obtain a precise equilibrium without having to move lower support assembly  30 . If a mode of operation is to have fulcrum  32  move independently of the fulcrum wheel  46 , the arrangement is the same with the exception that reversible clamping spacer  52  has an orientation 180 degrees from the  FIG. 4  illustration and clamps the inner race of the fulcrum anti-friction bearing  50  to a shoulder (not shown) on the fulcrum axle  38 , thereby allowing fulcrum  32  to rotate independently of the fulcrum wheel  46 . This mode of operation is desirable when the moveable fulcrum assembly  22  in being translated longitudinally with a hoist or crane. 
     Once this equilibrium state is realized, the hoist or crane is returned to a perpendicular position relative to radial projection  20 , the distance is measured from a laser  24  mounted on the plane of attachment of radial projection  20  to planar target  23 , which is now coincident with its center of gravity and the rotational axis of fulcrum  32 . In this state of equilibrium, the total weight is also measured by hoisting moveable fulcrum assembly  22  such that weight of radial projection  20  is no longer supported by fulcrum wheels  46  and summing the forces a arm load cell  28  located at opposite ends of moveable fulcrum assembly  22  between hoist separator plate  44  and upper fulcrum support  48 . Furthermore, a predetermined distance has been established in the positioning of the chord wise direction of radial projection  20  along the rotational axis of fulcrum  32  from a preferred longitudinal axis on radial projection  20  to each of arm load cell  28  locations. 
     The measurements of force and distance are communicated to a computer where the span wise moment is calculated according to the sum of arm load cell  28  measurements which are biased to a zero force when moveable fulcrum assembly  22  is empty of radial projection  20  and not supported by fulcrum wheels  46 . With the predetermined distance of the preferred longitudinal axis to each of the respective lower support load cells  36 , the chord wise moment is calculated. The measurements and calculations are displayed on a terminal and stored to storage media. Once the process has been completed for all radial projections of a rotating assembly, a preferred span moment is chosen by to which all of the other radial projections will be adjusted. Practically, the maximum span moment of the radial projections is chosen as it is easier to add weight to the other radial projections than it is to remove it. Additionally, a preferred chord wise moment is chosen as the maximum chord wise moment of the radial projections for the same reason. 
     It should be appreciated that the communication between laser  24  and arm load cells  28  can be achieved by either a wired or wireless means as are both common in the measurement and process control art. It should also be appreciated that all measurements can be displayed numerically, graphically, or both as is common in the measurement and process control arts. It should be further appreciated that any data obtained can be stored and retrieved by any means common in the art of data processing. 
     It is desirable to add a minimum amount of weight to correct both the span wise moment and cord wise moment to the preferred span wise and preferred chord wise moment. For each radial projection  20 , the corrective weight necessary to obtain the preferred chord wise moment is subtracted from the corrective weight necessary to obtain the preferred span wise moment. The resulting corrective span wise weight is then placed at a distance off of the preferred longitudinal axis such that the product of the resulting corrective span weight and the chord wise off axis distance equals the preferred cord wise moment. Simultaneously, the longitudinal placement of the resulting corrective weight will result in the preferred span moment. 
     Description— FIGS. 5 ,  6 ,  6 A Preferred Embodiment 
     Another embodiment of the invention is used to find a series of span wise and chord wise moments along the entire length of radial projection  20  to establish a profile of span wise and chord wise moments verses distance. By dividing each span wise moment by its respective distance and each chord wise moment by its chord wise distance, a profile of weight distribution can be plotted for the entire length of radial projection  20 . This profile can be compared to profiles of other radial projections. 
       FIG. 5  illustrates an isometric view of another embodiment. In this embodiment, the illustration shows moveable fulcrum assembly  22  supported by lower fulcrum support assembly  30  and a perpendicularly bi-axial fulcrum assembly  58  connected to the plane of attachment of radial projection  20  with an axial attachment plate  62 . The height of perpendicularly bi-axial fulcrum assembly  58  can be adjusted with a hydraulic cylinder  60  and a hydraulic ram  64  connected to perpendicularly bi-axial fulcrum assembly  58  such that there is no attitude change in radial projection  20  as moveable fulcrum assembly  22  translates the span of radial projection  20 . Due to its bi-axial nature, the only span wise and chord wise moment reactions around the plane of attachment of radial projection  20  will be at moveable fulcrum assembly  22 . The pressure of the hydraulic cylinder is measured by a pressure transducer  68 . The force that is produced by hydraulic ram  64  can be calculated by dividing the measured pressure by the cross sectional surface area of hydraulic ram  64 . This force is necessarily the force acting through the perpendicularly bi-axial fulcrum assembly  58 . Since this force is the moment around moveable fulcrum assembly  22 , the location of moveable fulcrum assembly  22  is at the center of gravity when this force is zero. 
     It should be appreciated that axial attachment plate  62  can be fashioned to match any configuration required to properly mount radial projection  20  in a manner consistent with its mounting to a rotating assembly. It should also be appreciated that a plurality of moveable fulcrum assemblies could be used in the event that the structure of radial projection  20  will not support its own weight at any point along its span and not depart either from the principle of operation or the scope of the invention. 
     In operation of the invention in this embodiment moveable fulcrum assembly  22  is translated along the span wise direction of radial projection  20 . It should be appreciated that the translation of moveable fulcrum assembly  22  can be accomplished in a variety of manners e.g. applying linear torque to lower fulcrum support assembly  30  with a winch or hoist or having lower fulcrum support assembly  30  powered by an electric or hydraulic motor. The lower fulcrum support assembly  30  could be modified such that it is necessarily guided by a track to assure its relational movement to radial projection  20  and the perpendicularly bi-axial fulcrum assembly  58 . 
     The distance is measured from laser  24  mounted on the plane of attachment of radial projection  20  to planar target  23  is continuously communicated to a computer as are the forces at lower support load cell  36  located at opposite ends of moveable fulcrum assembly  22  between upper fulcrum support  48  and lower fulcrum support assembly  30 . Additionally, the pressure from pressure transducer  68  connected to hydraulic cylinder  60  is continuously communicated to the computer to use this embodiment as a method to balance radial projection  20  as will be described later. A predetermined distance has been established in the positioning of the chord wise direction of radial projection  20  along the rotational axis of fulcrum  32  from a preferred longitudinal axis on radial projection  20  to each of the load cell locations. When the computer registers a change in distance as communicated by the laser and the change exceeds a predefined threshold established by the user, the computer displays and stores the measurement of the longitudinal distance and the measurement of forces at lower support load cells  36 , and the pressure at pressure transducer  68  of hydraulic cylinder  60  and calculates, stores, and displays the span wise and chord wise moments about the perpendicularly bi-axial fulcrum assembly  58 . This process continues until moveable fulcrum assembly  22  translates the entire span of radial projection  20 . 
     As moveable fulcrum assembly  22  translates the span of radial projection  20 , the pressure in hydraulic cylinder  60  will change as it is the reaction moment force of the radial projection  20  around the moveable fulcrum assembly  22 . At some point in the translation, the pressure will be zero. At this point, moveable fulcrum assembly  22  will be at the center of gravity of radial projection  20 . Since all of the data necessary to balance radial projection  20 , as described previously in the other embodiments, is acquired throughout the translation of moveable fulcrum assembly  22 , the data can be either retrieved at this exact point or interpolated from the data series. Thus, this embodiment can provide not only a profile of span wise moments and chord wise moments for the entire span of radial projection  20  as well as the derived weight distribution but will necessarily include the data to balance radial projection  20  at its center of gravity. Furthermore, this embodiment can be automated as is common in the art of process control such that all of the operation described can be achieved without human intervention and without departing from the scope of the invention. 
     It should be appreciated that the communication between laser  24  and lower support load cell  36  can be achieved by either a wired or wireless technology as are both common in the measurement and process control art. It should also be appreciated that all measurements can be displayed numerically, graphically, or both as is common in the measurement and process control arts. It should be further appreciated that any data obtained can be stored and retrieved by any means common in the art of data processing. Furthermore, the data obtained can be assigned to a mathematical model of the mechanical structure of radial projection  20  for evaluation. Additionally, any profile can be retrieved and compared to a newly acquired profile.