Patent Document

TECHNICAL FIELD 
   The present invention generally relates to prognostic health monitoring of an air cycle machine (ACM) for an aircraft, and more particularly relates to predicting ice formation and shedding on ACM turbine blades, and resulting wear on ACM journal bearings. 
   BACKGROUND 
   Air cycle machines (ACM) are used in many aircraft environmental control systems (ECS). The ECS, as is generally known, is used to manage cooling, heating, and pressurization of the aircraft. The ACM typically takes the form of a compact, rotary compressor based system, and may include a compressor, a heat exchanger, a fan, a turbine with blades and bearings, such as journal bearings, and a shaft connecting the compressor, fan and turbine. The ACM compressor receives compressed ambient air from an engine compressor or auxiliary power unit, further compresses the air, and supplies the further compressed air to the ACM turbine. The further compressed air expands through the ACM turbine, providing power as well as a cool, fresh air supply for the aircraft. 
   ACMs, like many apparatus, are susceptible to wear, and are a relatively expensive ECS part to repair and overhaul. One source of wear for ACMs results from ice formation and shedding on ACM turbine blades. This ice formation and shedding on the ACM turbine blades can result in imbalance conditions for the ACM turbine blades, causing wear to ACM journal bearings. The ice formation and shedding, and resulting ACM bearing wear, is difficult to accurately predict due to dynamic conditions in the ACM, and such ACM wear is generally not detected until after the wear has become significant enough so as to have noticeable deleterious effects on the ACM. Once these noticeable deleterious effects have occurred, the ACM can become much more expensive to repair. 
   Accordingly, there is a need for a method and apparatus to accurately predict ice formation and shedding, and resulting ACM wear, under dynamic conditions associated with an ACM. 
   BRIEF SUMMARY OF THE INVENTION 
   A method is provided for predicting ice formation on and shedding from blades of an air cycle machine (“ACM”) turbine. The method comprises generating operational condition data representative of ACM turbine operating conditions using a software model of the ACM. An amount of ice formation on the blades of the ACM turbine is determined, based at least in part on the generated operational condition data. An amount of ice shed from the blades of the ACM turbine is determined, based at least in part on the determined amount of ice formation and the generated operational condition data. In one embodiment, the determined amount of ice formation and ice shed is used to predict an amount of wear for the ACM. 
   An apparatus is also provided for predicting ice formation on and shedding from blades of an ACM turbine. The apparatus comprises means for generating operational condition data representative of ACM turbine operating conditions using a software model of the ACM, means for determining an amount of ice formation on the blades of the ACM turbine, based at least in part on the generated operational condition data, and means for determining an amount of ice shed from the blades of the ACM turbine, based at least in part on the determined amount of ice formation and the generated operational condition data. In one embodiment, the apparatus may also comprise means for determining an amount of wear for the ACM, based at least in part on the amount of ice formation and shed. 

   
     BRIEF DESCRIPTION OF THE DRAWINGS 
     The present invention will hereinafter be described in conjunction with the following drawing figures, wherein like numerals denote like elements, and 
       FIG. 1  provides a schematic depiction of an air cycle machine (ACM); 
       FIG. 2  provides a method of prediction ice formation and shed on ACM turbine blades in a preferred embodiment; 
       FIG. 3  depicts a flowchart with a more detailed depiction of a step  56  of the method of  FIG. 2  in a preferred embodiment; 
       FIG. 4  depicts a flowchart with a more detailed depiction of intermediate step  66  from step  56  of  FIG. 3  in a preferred embodiment; 
       FIG. 5  depicts two formulas pertaining to collection efficiency calculations from  FIGS. 4 and 5  in a preferred embodiment; 
       FIG. 6  depicts an illustrative graph for an application of the method of  FIG. 2 , namely a turbine gas path temperature graph; 
       FIG. 7  depicts an illustrative graph for an application of the method of  FIG. 2 , namely a turbine entrained moisture graph; 
       FIG. 8  depicts an illustrative graph for an application of the method of  FIG. 2 , namely an ice formation graph; 
       FIG. 9  depicts an illustrative graph for an application of the method of  FIG. 2 , namely a first order lag turbine entrained moisture graph; 
       FIG. 10  depicts an illustrative graph for an application of the method of  FIG. 2 , namely a first order lag ice formation graph; 
       FIG. 11  depicts an illustrative graph for an application of the method of  FIG. 2 , namely a first order lag shedding frequency graph; 
       FIG. 12  depicts an illustrative graph for an application of the method of  FIG. 2 , namely a first order lag maximum ice graph; and 
       FIG. 13  depicts an additional application of the method of claim  2  with respect to calculation of an amount of cumulative wear for an ACM. 
   

   DETAILED DESCRIPTION OF THE INVENTION 
   The following detailed description of the invention is merely exemplary in nature and is not intended to limit the invention or the application and uses of the invention. Furthermore, there is no intention to be bound by any theory presented in the preceding background of the invention or the following detailed description of the invention. 
     FIG. 1  provides a schematic depiction of an air cycle machine (ACM)  10 . In the depicted embodiment, the ACM  10  includes a compressor  12 , a heat exchanger  14 , a fan  16 , a turbine  18 , and a shaft  20  that connects the compressor  12 , the fan  16 , and the turbine  18 . During ACM  10  operation, the compressor  12  receives a flow of air  21  from an engine compressor or auxiliary power unit (not shown) and further compresses the air  21 , thereby further heating the compressed air  21 . The air  21  is then delivered to the heat exchanger  14 , where the air  21  is cooled by the fan  16  by drawing cooler air through a portion of the heat exchanger  16 . The air  21  is then delivered to the turbine  18 , which expands the air  21 . As the air  21  expands across turbine blades  22  in the turbine  18 , the turbine  18  generates power to drive the compressor  12  and the fan  16 , and additionally cools the air  21 . The cooled air  21  is then used to cool and condition the aircraft cabin (not shown). The turbine  18  is rotationally mounted via a plurality of bearings, such as journal bearings  24 . 
   Moving now to  FIG. 2 , a flowchart is depicted of an icing prediction process  26  for predicting an amount of ice formation  28  and ice shed  30  on the blades  22  of the ACM turbine  18 . In the depicted embodiment the process  26  begins by obtaining aircraft operating data  32 . The aircraft operating data  32  represents certain operating conditions of an aircraft such as, for example, air temperature, humidity, and altitude, and can be obtained from sensors aboard an aircraft. However, it will be appreciated by one of skill in the art that various other aircraft operating data  32  may be used, and that the aircraft operating data  32  may be generated by any one of numerous types of sensors or other apparatus or systems. Regardless of its specific makeup and how it is obtained, the operating data  32  is supplied to an ACM model  34 , which generates turbine conditions data  36  representing operational conditions of the ACM turbine  18 . The turbine conditions data  36  are in turn supplied to an icing model  38 , which determines the amount of ice formation  28  and ice shed  30  on turbine blades  22 . Each of the steps in this generalized process is described in greater detail below. 
   As depicted in  FIG. 2 , the aircraft operating data  32  can first be supplied to a performance model  40  in step  38 , and to the ACM model  34  in step  44 . In step  46  the performance model  40  can be used to determine boundary conditions  48  for the ACM  10 , which can be determined at least in part utilizing the aircraft operating data  32  supplied to the performance model  40  in step  38 . Next, in step  50 , the boundary conditions  48  can be supplied to the ACM model  34 . In certain preferred embodiments the performance model  40  can include an aircraft engine performance model and/or an auxiliary power unit performance model; however, it will be appreciated that any number of particular performance models  40  can be used to derive boundary conditions for the ACM  10 . It will be appreciated that various steps in the icing prediction process  26 , including for example steps  44  and  50 , among other steps, need not occur in the same order in which the steps are numbered or otherwise referenced herein. 
   In step  52 , the ACM model  34  preferably uses the aircraft operating data  32  and the boundary conditions  48  to generate the turbine conditions data  36 . The turbine conditions data  36  represents operational conditions of the ACM turbine  18  such as, for example, temperature, pressure, and entrained moisture of air for the turbine  18 . It will be appreciated that the turbine conditions data  36  may represent various other conditions that may also have an effect on the amount of ice formation  28  and ice shed  30 . Preferably the ACM model  34  is a software-based model which uses the boundary conditions  48  to more accurately model the relationship between the aircraft operating data  32  and the turbine conditions data  36 . However, it will be appreciated that the ACM model  34  and the performance model  40  can take any one of numerous different forms, and that in certain embodiments the ACM model  34  may not use a performance model  40  and/or boundary conditions  48 . Regardless of the type of the ACM model  34  and/or performance model  40  used, the generated turbine conditions data  36  are used by the icing model  38  to determine the amount of ice formation  28  on and ice shed  30  from the ACM turbine blades  22 . 
   Specifically, in step  54  the turbine conditions data  36  are supplied to the icing model  38 . Next, in step  56 , the amount of ice formation  28  and ice shed  30  are determined using the icing model  38 , as set forth in greater detail below and in  FIG. 3 . Next, in step  58  of a preferred embodiment, an amount of ACM wear  60  can be determined based at least in part on the amount of ice formation  28  and ice shed  30 . In a preferred embodiment, the amount of ACM wear  60  can be determined based at least in part on wear to the ACM journal bearings  24 , which can be caused by imbalance conditions that can result from ice formation on and shedding from the ACM turbine blades  22 . Finally, in step  62  of a preferred embodiment, the determined ACM wear  60  values can be aggregated over a predetermined period of time, in order to determine an amount of cumulative wear  64  for the ACM  10 . One particular embodiment for determining the amount of cumulative wear  64  is discussed later in connection with  FIG. 13 , However, it will be appreciated that various measures of ACM wear  60  may be used, and the amount of cumulative wear  64  may be determined in any one of a number of different manners. 
   Turning now to  FIG. 3 , a more detailed depiction of step  56  for a preferred embodiment is provided, showing intermediate steps  66 ,  68  and  70  in determining the amount of ice formation  28  and ice shed  30 . First, in step  66 , the icing model  38  calculates an amount of collected water  72  on the turbine blades  22 , based at least in part on the turbine conditions data  36  and typical water droplet size distribution information  74  from the icing model  38 . 
   The method by which the icing model  38  calculates the amount of water collected on turbine blades in step  66  is depicted in greater detail in  FIG. 4 . As shown therein, collection efficiency calculations are performed using the turbine conditions data  36  supplied in step  54 , which preferably includes values for turbine temperature  76 , pressure  78  and entrained moisture  80  of air surrounding the ACM turbine  18 . As will be discussed later in connection with  FIG. 7 , these values can further be divided, for example, by using different temperature  76  values for different regions of the turbine  18 . The turbine conditions data  36  are used to compute collection efficiency, using a collection efficiency map  82 , which models collection efficiency  84  versus water droplet size. As is commonly known, and as set forth in formula  86  of  FIG. 5 , the collection efficiency  84  represents a ratio of the amount of the collected water  72  on a surface to the amount of entrained moisture  80  in surrounding air. As depicted in  FIGS. 4 and 5 , when combined with the typical water droplet size distribution information  74  that is supplied from the icing model  38 , the collection efficiency map  82  can be used to calculate values of the collection efficiency  84  for the ACM turbine  18 . The collection efficiency  84  values can then be combined with the values for the amount of entrained moisture  80  from the turbine conditions data  36  to calculate the amount of collected water  72  for the turbine blades  22 . This is done, for example, by multiplying the values for the collection efficiency  84  by the values for the entrained moisture  80  as shown in formula  88  of  FIG. 5 . In a preferred embodiment, the collected water calculations of step  66  may be based on an assumption that entrained moisture in air surrounding the ACM turbine blades  22  is the only source of water and ice formation on the ACM turbine blades  22 . 
   While  FIGS. 4 and 5  depict a preferred embodiment for calculating collected water, it will be appreciated that these calculations can take any one of numerous different forms. For example, the turbine conditions data  36  may include other values instead of, or in addition to, temperature  76 , pressure  78 , and entrained moisture  80 . It will be further appreciated that the droplet size distribution  74  values may be included at the time the icing model  38  is formed, or may be subsequently added and/or updated to the icing model  38 . Similarly, it will be appreciated that the assumptions underlying the collected water calculations may vary, resulting in somewhat different calculations which may include, by way of example, calculations pertaining to other sources of water and ice formation. Regardless of the specific variables, steps and assumptions used in the collected water calculations, the amount of collected water  72  is calculated in step  66 , for use in calculating the amount of ice formation  28  in step  68 . 
   Next, and returning now to  FIG. 3 , in step  68  the icing model  38  calculates the amount of ice formation  28  on the turbine blades  22 , preferably based at least in part on the amount of collected water  72  calculated in step  66 , and heat transfer parameters  90  from the icing model  38  representing heat transfer arising at least in part from air flow through the turbine  18 . As is commonly known, ice formation can occur, for example, when the collected or deposited water  72  freezes and accumulates on the ACM turbine blades  22 . In a preferred embodiment, the calculations in step  68  are based in part on assumptions that (i) the ACM turbine  18  represents a lumped heat capacity system and (ii) ice formation occurs uniformly over the turbine blades  22 . Based on these assumptions, the heat transfer parameters  90  are used, in connection with the calculated values for the collected water  72  on the ACM turbine blades  22  and the turbine conditions data  36 , to calculate the amount of ice formation  28  on the ACM turbine blades  22 . 
   It will be appreciated that the assumptions underlying the step  68  calculations may vary, resulting in somewhat different calculations which may include, by way of example, calculations pertaining to non-uniform ice formation. It will also be appreciated that various values of the turbine conditions data  36  may also be used in step  68  in combination with the calculated amount of collected water  72  from step  66  and the heat transfer parameters  90 , and that the heat transfer parameters  90  may be included at the time the icing model  38  is formed, or may be subsequently added and/or updated to the icing model  38 . Regardless of the specific values, assumptions and information used, and when the heat transfer parameters  90  are supplied to the icing model  38 , the amount of ice formation  28  is calculated in step  68 , for use in calculating the amount of ice shed  30  in step  70 . 
   Next, in step  70 , the icing model  38  calculates the amount of ice shed  30  for the ACM turbine blades  22 , preferably based at least in part on the amount of ice formation  28  calculated in step  68 , and values for maximum holding stress  92  of the ACM turbine blades  22 . As is commonly known, ice shedding can occur, for example, when ice formed on the turbine blades  22  is subjected to centrifugal force that exceeds a holding force of the ice on the blades  22 . In a preferred embodiment, the calculations in step  70  are performed by balancing the holding force with the centrifugal force, to determine the amount of ice shed  30 . In one such preferred embodiment, the centrifugal force is determined at a midpoint radius of the turbine blade  22 , while the corresponding amount of holding force is determined by the maximum holding stress  92  values of the ACM turbine blades  22  from the icing model  38 . 
   It will be appreciated that the assumptions underlying the step  70  calculations may vary, resulting in somewhat different calculations. It will also be appreciated that various values of the turbine conditions data  36  may also be used in step  70  in combination with the calculated amount of ice formation  28  and the maximum holding stress  92  values, and that the maximum holding stress  92  values may be included at the time the icing model  38  is formed, or may be subsequently added and/or updated to the icing model  38 . 
   As mentioned above, step  56 , including intermediate steps  66 ,  68  and  70 , can be conducted with any number of turbine conditions data  36 . For example, the turbine temperature  76  values can be separated into turbine downstream temperature  96  and turbine upstream temperature  98  values as shown in  FIG. 6  below, and the entrained moisture  80  values can be used to calculate separate turbine downstream entrained moisture  106  and upstream entrained moisture  108  values as shown in  FIG. 7 . Moreover, the results of the icing prediction process  26  can be used to calculate other icing values that are useful in graphical representation and analysis of the data, such as an amount of ice mass  116  remaining on the turbine blades  22 , a frequency of ice shedding  118 , and a maximum amount of ice  132  before shedding, as depicted in and discussed in connection with  FIGS. 8 ,  10 - 12  below. In addition, various techniques can be used, such as a first order lag model depicted in  FIGS. 9-12  below, to represent dynamic conditions for the ACM  10  that can cause time delay effects among one or more of the variables. These variations are discussed later in connection with the illustrative examples of graphical applications of the icing prediction process  16 , provided in  FIGS. 6-12 . 
   Regardless of the specific values, assumptions, techniques and information used in step  56 , the data obtained from the icing prediction process  26 , including the amount of ice formation  28  and ice shed  30 , can be subsequently used in determining various other icing characteristics, as well as the ACM wear  60 . For example, the icing prediction process  26  can be used, either onboard an aircraft or remotely, to calculate and monitor the amount of ice formation  28  and ice shed  30  for the ACM turbine blades  22  under dynamic conditions. This enables the calculation and monitoring of the amount of ACM wear  60  which, as mentioned above, can occur on the ACM journal bearings  24  as a result of the ice formation  28  and the ice shed  30  on the turbine blades  22 . The icing prediction process  26  can also be used to predict future ACM wear  60  based at least in part on information regarding flight patterns and history, and/or weather conditions or forecasts. 
   Also as mentioned above, the amount of ice formation  28 , ice shed  30 , and ACM wear  60  can be monitored using the icing prediction process  26  over an extended period of time for calculating and monitoring the cumulative wear  64  for the ACM  10 . This allows the ACM  10  to be replaced or repaired prior to experiencing noticeable deleterious effects, thereby enhancing ACM  10  performance and significantly reducing costs of replacing and/or repairing the ACM  10 . In addition, the icing prediction process  26  can also reduce costs in situations where the ACM  10  has not experienced substantial wear over a period of time, so that the ACM  10  need not be prematurely repaired or replaced. 
   As mentioned above,  FIGS. 6-12  depict illustrative graphical examples for a particular empirical application involving the icing prediction process  26 . As will be appreciated, the icing prediction process  26  can be used in any one of numerous different applications, and these examples are for illustrative purposes only. 
   First,  FIG. 6  depicts a turbine gas path temperature graph  94 , which is a graph of the turbine temperature  76  of the turbine  18  gas path, versus flight time. The turbine temperature  76  is preferably one of the turbine conditions data  36 , which is preferably determined at least in part by the ACM model  34  using the aircraft operating data  32 , and most preferably also using boundary conditions  48  calculated by the performance model  40 . As shown in  FIG. 6 , the turbine temperature  76  values can be separated into separate values, for example through separate measurements and/or calculations, for turbine downstream temperature  96  and turbine upstream temperature  98 , among various other potential categories and sub-categories of the turbine conditions data  36 .  FIG. 6  shows the turbine downstream temperature  96  values on curve  100 , and the turbine upstream temperature  98  values on curve  102 . 
     FIG. 7  depicts a turbine entrained moisture graph  104 , which is a graph of the entrained moisture  80  versus flight time. The entrained moisture  80  is preferably calculated in the intermediate step  66  of step  56  of the icing prediction process  26 . As shown in  FIG. 7 , the entrained moisture  80  values can be separated into separate values for turbine downstream entrained moisture  106  and turbine upstream entrained moisture  108 , for example through separate measurements and/or calculations based at least in part on the values for turbine downstream temperature  96  and turbine upstream temperature  98 , respectively.  FIG. 7  shows the turbine downstream entrained moisture  106  values on curve  110 , and the turbine upstream entrained moisture  108  values on curve  112 . 
     FIG. 8  depicts an ice formation graph  114 , which is a graph of an amount of ice mass  116  on the turbine blades  22  versus flight time. The amount of ice mass  116  for any given point in time can be calculated based on the amount of ice formation  28  and ice shed  30  determined in step  56  of the icing prediction process  26 . For example, for any particular point in time, the amount of ice mass  116  can be calculated at least in part by subtracting the amount of ice shed  30  from the amount of ice formation  28  for the turbine blades  22 . As shown in  FIG. 8 , when graphed against flight time, the amount of ice mass  116  can be used in calculating a frequency of ice shedding  118 . The amount of ice mass  116  is measured in pounds in  FIG. 8 ; however, it will be appreciated that this and/or other variables can be measured in any number of different types of units. As shown, the frequency of ice shedding  118  in this particular example ranged from 0.067 Hz to 16 Hz. 
     FIGS. 9-12  depict an extension of the application of  FIGS. 6-8 , in which a time lag is introduced to the model. A time lag can be useful, for example, in incorporating effects of thermal dynamics upstream of the ACM  10 . For example, certain aircraft operating data  32  and/or turbine conditions data  36  may have a delayed effect on the ACM  10  or the turbine blades  22  thereof, which can be more accurately represented by a model incorporating a time lag. 
     FIG. 9  depicts, for illustrative purposes, a first order lag (FOL) turbine entrained moisture graph  120 . As with the turbine entrained moisture graph  104  of  FIG. 7 , the FOL turbine entrained moisture graph  120  also is a graph of entrained moisture  80 , separated into turbine downstream entrained moisture  106  and turbine upstream entrained moisture  108 , versus flight time in seconds. However, the FOL turbine entrained moisture graph  120  includes a first order lag for turbine temperature  76 , with a time constant of 60 seconds.  FIG. 9  shows the turbine downstream entrained moisture  106  on curve  122 , and the turbine upstream entrained moisture  108  on curve  124 . It will be appreciated that various other time constants, lag modeling techniques and/or other techniques can be used to simulate time-delayed effects or other dynamic conditions affecting the ACM  10 , and that such techniques can be used in  FIG. 9  as well as  FIGS. 10-12  below, which, for illustrative purposes only, also include a first order time lag for turbine temperature  76 . 
     FIG. 10  depicts a first order lag (FOL) ice formation and shedding graph  126 . As with the ice formation graph  114  of  FIG. 8 , the FOL ice formation graph  126  also is a graph of the amount of ice mass  116  on the turbine blades  22  versus flight time, which can be used in calculating the frequency of ice shedding  118 . However, similar to  FIG. 9 , the FOL ice formation graph  126  of  FIG. 10  also includes a first order lag for turbine temperature  76 , with a time constant of 60 seconds. As shown, in this particular example the frequency of ice shedding  118  ranged from 0.0106 Hz to 0.124 Hz with the first order time lag. 
     FIG. 11  depicts a first order lag (FOL) shedding frequency graph  128 , which is a graph of the frequency of ice shedding  118  versus flight time in seconds, using the first order lag for turbine temperature  76  of  FIGS. 9-10 . The values for the frequency of ice shedding  118  depicted in  FIG. 11  can be extracted from the FOL ice formation graph  126 , as shown in  FIGS. 10-11 . 
   Similarly,  FIG. 12  depicts a first order lag (FOL) maximum ice graph  130 , which is a graph of values for a maximum amount of ice  132  that can accumulate before shedding occurs versus flight time, using the first order lag for turbine temperature  76  of  FIGS. 9-11  As shown, the maximum amount of ice  132  is measured in pounds in  FIG. 12 . However, as mentioned above, it will be appreciated that the values, as for any of the other variables, can be measured in any number of different types of units. Regardless of the units of measurement, the maximum amount of ice  132  can be calculated from the amount of ice mass  116  from the (FOL) ice formation graph  126  of  FIG. 10 . As with various other variables mentioned above, the maximum amount of ice  132  before shedding can also serve as a valuable tool, for example, in controlling operating conditions of the ACM  10  so as to control the amount of ice shed  30  from the ACM turbine blades  22 , among various other potential applications. 
   Turning now to  FIG. 13 , another application of the icing prediction process  26  is shown. In the particular embodiment depicted in  FIG. 13 , the amount of cumulative wear  64  for the ACM  10  can be determined through various calculations based at least in part on the amount of ice formation  28  and ice shed  30 , and/or various related variable values  134 , such as those depicted in  FIGS. 6-12  above. First, an amount of imbalance force (over time)  136  can be calculated based on the values for the amount of ice formation  28  and ice shed  30 , and/or from related variable values  134  such as the amount of ice mass  116 , the frequency of ice shedding  118 , and the maximum amount of ice  132 . The amount of imbalance force  136  can in turn be used to calculate an amount of transmitted force (over time)  138  to the journal bearings  24 . The amount of transmitted force  138  can in turn be used, alone or in conjunction with the aircraft operating data  32  and/or other variables, to determine an amount of total force (over time)  140  to the journal bearings  24 . In addition, a bearing load capacity  142  for the journal bearings  24  can be calculated from the aircraft operating data  32  and/or other variables. Finally, the amount of cumulative wear  64  for the ACM  10  can be calculated at least in part from the total force  140  and the bearing load capacity  142  for the journal bearings  24 . As mentioned above,  FIG. 13  shows one application of the icing prediction process  26  for illustrative purposes only. It will be appreciated that the amount of cumulative wear  64  can be calculated using any one of numerous techniques using the results of the icing prediction process  26 , and it will further be appreciated that the icing prediction process  26  may have numerous different applications. 
   While at least one exemplary embodiment has been presented in the foregoing detailed description of the invention, it should be appreciated that a vast number of variations exist. It should also be appreciated that the exemplary embodiment or exemplary embodiments are only examples, and are not intended to limit the scope, applicability, or configuration of the invention in any way. Rather, the foregoing detailed description will provide those skilled in the art with a convenient road map for implementing an exemplary embodiment of the invention, it being understood that various changes may be made in the function and arrangement of elements described in an exemplary embodiment without departing from the scope of the invention as set forth in the appended claims and their legal equivalents.

Technology Category: f