Patent Publication Number: US-2018051624-A1

Title: Apparatus, system, and method for shaping a valve orifice

Description:
FIELD 
     This invention relates to methods of fluid dynamic control and more particularly relates to a method for shaping a valve orifice. 
     BACKGROUND 
     Valves perform an important and integral function for most fluid control schemes. Present combustion engines rely on an array of valves to regulate the flow of fluids throughout the engine&#39;s various systems. Valves perform a critical role regulating the flow of fluids to achieve emissions control standards, fuel efficiency, engine braking, and protection of engine components. 
     A common valve utilized presently in many applications is the rotary valve. A typical rotary valve consists of a stationary structure placed in-line with a fluid flow and a rotating sleeve configured such that the rotating sleeve may be turned to various angles, each angle corresponding to a specific fluid flow. The rotating sleeve contains a flow-through passage with an intake orifice and an outlet orifice. The orifices are generally shaped as conveniently as possible, such as an oval or a rectangle. When the sleeve passage is fully in-line with the fluid flow the valve may be considered to be fully open. When the sleeve is rotated such that a wall of the sleeve fully blocks the passage (no section of the orifice is exposed to the passage) the valve may be considered to be fully closed. At intermediate valve positions, a rotary valve may provide an intermediate restriction between fully open and fully closed. In practice, the flow rate through the valve is highly non-linear, providing rapidly increasing flow as the valve is slightly opened, and very little flow increase beyond a medium-opened valve. 
     Designing control algorithms to take advantage of the rotary valve&#39;s continuous range of fluid flows introduces challenges. For example, a valve controller may comprise an analog to digital controller that uses a voltage to communicate with the valve controller. For example, a voltage range of 0 to 5 volts may correspond to the 5 volts being a fully closed position of the valve and the 0 volts corresponding to a fully open position of the valve. A typical valve controller may assign 10 bits of memory, with 1,024 different values for position, for commanding a valve position, and assign 6 bits, with 64 different values, for providing diagnostics. Of the 1,024 possible value positions, typically only the first 100 are relevant as a 10% opened valve may already allow 60% or more of the total flow. Further, the electronics of the system may allow the true valve position to be detected only within +/−0.2 volts (in one example), meaning that the valve really only has about 25 available positions in resolvable increments of +/−40 of the original 1.024 possible valve positions. 
     As a further complication, some systems utilize the valve in a non-linear fashion, requiring some flow regimes preferentially over other flow regimes. For example, a system may require flow areas of about 0-10% open about 50% of the time, and flow areas of about 85-100% open about 50% of the time, but rarely require flow areas between 10% and 85%. When the non-linearity of use is combined with the physical non-linearity of flow in a typical rotary valve, it is clear that a rotary valve used in the current art has complications in control, uniformity of usage, and durability through asymmetrical usage. 
     One specific example occurs in an internal combustion engine application. Some diesel engines utilize two turbochargers in series, with a small responsive (high pressure) turbocharger in line with a large slower responding (low pressure) turbocharger. At very low flow rates, the small turbocharger is utilized to provide a responsive engine to operator torque requests. At higher flow rates, the smaller turbocharger is bypassed and the larger turbocharger dominates the air flow workload for the engine. A typical bypass valve in the industry is a rotary valve. When the speed-load map of the engine is considered, and the amount of time that an engine spends at various workloads is considered, it is apparent that a rotary bypass valve for a high pressure turbocharger suffers from the control drawbacks of current rotary valves. At low flow rates, the controller is utilizing only a few bits of the available valve position commands, and suffering from a high signal to noise ratio as many of the assignable bits for valve position are not utilized. At high flow rates, the controller is merely opening the bypass valve completely and utilizing the 100%-open commands. Therefore, a typical rotary valve in a diesel application provides a highly non-linear response with a high signal-to-noise ratio, and also does not utilize the middle range of the rotary valve positions. 
     SUMMARY 
     From the foregoing discussion, it should be apparent that a need exists for an apparatus, system, and method to simplify control of rotary valves. Beneficially, such an apparatus, system, and method would permit a uniform movement of a valve for a correspondingly uniform change in an output characteristic such as fluid flow, and/or provide for uniform utilization of the valve through the operating range of an application. 
     The present invention has been developed in response to the present state of the art, and in particular, in response to the problems and needs in the art that have not yet been fully solved by currently available rotary valves. Accordingly, the present invention has been developed to provide an apparatus, system, and method for shaping a valve orifice that overcome many or all of the above-discussed shortcomings in the art. 
     According to one representative embodiment, a method for optimizing an orifice shape includes determining a specified relationship between a valve position and an output characteristic. The method also includes determining an orifice profile comprising a relationship of an orifice area to the output characteristic. Additionally, the method includes shaping an orifice in a valve based on the orifice profile and the specified relationship between the valve position and the output characteristic. The orifice is shaped in this manner such that the valve exhibits approximately the specified relationship. In some implementations, the output characteristic includes a relative flow rate of fluid through the valve and/or a relative coverage of at least a portion of a torque-speed map. In yet some implementations, the specified relationship includes a linear relationship between the valve position and the relative flow rate of fluid through the valve and/or a linear relationship between the valve position and the relative coverage of at least a portion of the torque-speed map. 
     According to certain implementations, the orifice area includes one of a projected exposed area (PEA) and an effective flow area (EFA). In some implementations where the orifice area includes a PEA, determining the orifice profile includes determining the output characteristic for the PEA from a calibration valve. In some implementations where the orifice area includes an EFA, determining the orifice profile includes determining the output characteristic for the EFA from a computational fluid dynamics model. 
     In some implementations of the method, shaping the orifice in a valve includes shaping a closest physically realizable orifice in a valve, a best-fit triangular approximation, and a best-fit approximation of easily-machined shapes. 
     The shaped orifice discussed above can, in some implementations, include a first orifice. In these implementations, the method can also include determining a performance curve for the first orifice where the performance curve includes an exhibited relationship between the valve position and the output characteristic for the first orifice. The method can further include determining an improvement index for the first orifice based on the performance curve and the specified relationship. Additionally, the method can include generating a second orifice profile based on the improvement index and the orifice profile such that the second orifice profile exhibits an improved performance curve for the second orifice. 
     According to another embodiment, an apparatus for optimizing an orifice shape includes a specified relationship module, an orifice profile module, and an orifice shaping module. The specified relationship module is configured to determine a valve orifice position for an output characteristic. The orifice profile module configured to produce an orifice profile for the specified relationship. The orifice shaping module configured to produce an orifice shape based on the orifice profile and the specified relationship. In some implementations, the specified relationship includes an approximately linear relationship between rate of fluid flow through a valve and a valve position. In other implementations, the specified relationship includes an approximately linear relationship between an accumulated area under a torque-speed map and a valve position. 
     In another embodiment, an apparatus for optimizing an orifice shape includes a valve and a valve orifice. The valve orifice is shaped by a process that includes determining a specified relationship between a valve position and an output characteristic, determining an orifice profile comprising a relationship of an orifice area to the output characteristic, and shaping an orifice in a valve based on the orifice profile and the specified relationship between the valve position and the output characteristic such that the valve exhibits approximately the specified relationship. 
     In some implementations, the valve is a rotary valve. In yet some implementations, the valve orifice is shaped such that for every degree radius of turn of the valve a substantially uniform change in a fluid flow through the valve is achieved. The valve orifice can be shaped such that for every degree radius of turn of the valve a substantially uniform change in a torque-speed map is achieved. Additionally, the valve orifice can have a shape configured as a best-fit approximation of easily manufactured shapes. In certain implementations, the valve orifice is a best-fit triangle. 
     According to yet another embodiment, a system for optimizing a valve for configurable response includes an internal combustion engine, a turbocharger; and a rotary valve having an optimized orifice profile. The orifice profile is optimized by determining a specified relationship between a desired valve orifice position and a desired output characteristic, determining an orifice profile based on an orifice area for the desired output characteristic, and shaping an orifice in the valve based on the orifice profile and the specified relationship between the desired valve orifice position and the desired output characteristic. The shape of the orifice is such that the valve exhibits approximately the specified relationship. The rotary valve of the system can be one of a barrel valve and a bypass valve. Further, the orifice can have the shape of a best fit triangle. 
     Reference throughout this specification to features, advantages, or similar language does not imply that all of the features and advantages that may be realized with the present invention should be or are in any single embodiment of the invention. Rather, language referring to the features and advantages is understood to mean that a specific feature, advantage, or characteristic described in connection with an embodiment is included in at least one embodiment of the present invention. Thus, discussion of the features and advantages, and similar language, throughout this specification may, but do not necessarily, refer to the same embodiment. 
     Furthermore, the described features, advantages, and characteristics of the invention may be combined in any suitable manner in one or more embodiments. One skilled in the relevant art will recognize that the invention may be practiced without one or more of the specific features or advantages of a particular embodiment. In other instances, additional features and advantages may be recognized in certain embodiments that may not be present in all embodiments of the invention. 
     These features and advantages of the present invention will become more fully apparent from the following description and appended claims, or may be learned by the practice of the invention as set forth hereinafter. 
    
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
       In order that the advantages of the invention will be readily understood, a more particular description of the invention briefly described above will be rendered by reference to specific embodiments that are illustrated in the appended drawings. Understanding that these drawings depict only typical embodiments of the invention and are not therefore to be considered to be limiting of its scope, a description and explanation of various embodiments of the invention with additional specificity and detail will be aided through the use of the accompanying drawings, in which: 
         FIG. 1  is a schematic illustration depicting one embodiment of a system to design a valve orifice profile: 
         FIG. 2A  is an illustration depicting one example of a typical or conventional valve orifice profile; 
         FIG. 2B  is an illustration depicting one example of an optimal valve orifice profile; 
         FIG. 2C  is an illustration depicting one example of a best-fit valve orifice profile; 
         FIG. 2D  is an illustration depicting an alternate example of an optimal valve orifice profile; 
         FIG. 2E  is an illustration depicting one example of a best-fit triangle valve orifice profile; 
         FIG. 2F  is an illustration depicting an alternate example of a best-fit triangle valve orifice profile; 
         FIG. 3A  is a graph illustrating one embodiment of a torque-speed map for an expected engine duty cycle with a typical valve orifice profile; 
         FIG. 3B  is a graph illustrating one embodiment of a torque-speed map for an expected engine duty cycle with a shaped valve orifice profile: 
         FIG. 4A  is a graph illustrating one embodiment of a torque-speed map for an expected engine duty cycle with a typical valve orifice profile: 
         FIG. 4B  is a graph illustrating one embodiment of a torque-speed map for an expected engine duty cycle with a shaped valve orifice profile; 
         FIG. 5A  is a graph illustrating one embodiment of a torque-speed workspace area histogram for a valve position; 
         FIG. 5B  is a graph illustrating one embodiment of a high resolution torque-speed workspace area histogram for a valve position; 
         FIG. 6  is a graph illustrating one embodiment of a torque-speed workspace cumulative usage for a valve position; 
         FIG. 7  is a graph illustrating an alternate embodiment of a high resolution torque-speed workspace area histogram for a valve position; 
         FIG. 8  is a graph illustrating an example of a high resolution torque-speed workspace cumulative usage for a valve position; 
         FIG. 9  is a table illustrating one embodiment of required input for optimizing an orifice shape; 
         FIG. 10  is an illustration depicting one embodiment of a closed valve geometry; 
         FIG. 11  is an illustration depicting one embodiment of a partially open valve geometry; 
         FIG. 12  is a graph illustrating one embodiment of a reshaping of a typical valve orifice; 
         FIG. 13  is a schematic block diagram depicting one embodiment of a method for shaping a valve orifice; 
         FIG. 14  is a schematic block diagram depicting another embodiment of a method for shaping a valve orifice; and 
         FIG. 15  is a schematic block diagram depicting yet another embodiment of a method for shaping a valve orifice. 
     
    
    
     DETAILED DESCRIPTION 
     Many of the functional units described in this specification have been labeled as modules, in order to more particularly emphasize their implementation independence. For example, a module may be implemented as a hardware circuit comprising custom VLSI circuits or gate arrays, off-the-shelf semiconductors such as logic chips, transistors, or other discrete components. A module may also be implemented in programmable hardware devices such as field programmable gate arrays, programmable array logic, programmable logic devices or the like. 
     Modules may also be implemented in software for execution by various types of processors. An identified module of executable code may, for instance, comprise one or more physical or logical blocks of computer instructions which may, for instance, be organized as an object, procedure, or function. Nevertheless, the executables of an identified module need not be physically located together, but may comprise disparate instructions stored in different locations which, when joined logically together, comprise the module and achieve the stated purpose for the module. 
     Indeed, a module of executable code may be a single instruction, or many instructions, and may even be distributed over several different code segments, among different programs, and across several memory devices. Similarly, operational data may be identified and illustrated herein within modules, and may be embodied in any suitable form and organized within any suitable type of data structure. The operational data may be collected as a single data set, or may be distributed over different locations including over different storage devices, and may exist, at least partially, merely as electronic signals on a system or network. 
     Reference throughout this specification to “one embodiment,” “an embodiment,” or similar language means that a particular feature, structure, or characteristic described in connection with the embodiment is included in at least one embodiment of the present invention. Thus, appearances of the phrases “in one embodiment,” “in an embodiment,” and similar language throughout this specification may, but do not necessarily, all refer to the same embodiment. 
     Furthermore, the described features, structures, or characteristics of the invention may be combined in any suitable manner in one or more embodiments. In the following description, numerous specific details are provided, such as examples of programming, software modules, user selections, network transactions, database queries, database structures, hardware modules, hardware circuits, hardware chips, etc., to provide a thorough understanding of embodiments of the invention. One skilled in the relevant art will recognize, however, that the invention may be practiced without one or more of the specific details, or with other methods, components, materials, and so forth. In other instances, well-known structures, materials, or operations are not shown or described in detail to avoid obscuring aspects of the invention. 
       FIG. 1  is a schematic illustration depicting one embodiment of a system  100  to shape a valve orifice. The system  100  includes an engine  102  that may be a gasoline engine, diesel engine, combustion engine, or any type of engine producing a fluid flow  104 . The system  100  further includes a turbine device  106 . In one embodiment, the turbine device  106  is a turbocharger. Additionally, the system  100  includes a rotary valve  108 . The rotary valve may be a barrel valve configured as a bypass valve for the turbocharger  106 . The opening and closing of the bypass valve  108  may be initiated by an engine control module (ECM), e.g., controller  110 . The bypass valve  108  may be configured to be rotated to a plurality of valve positions corresponding to a plurality of rates of fluid flow through the valve  108 . 
     The controller  110  includes modules configured to determine a specified relationship between a valve position and an output characteristic, create a valve orifice profile based on the specified relationship, and optimize the orifice profile to a best-fit configuration. The controller  110  may comprise a specified relationship module, an orifice profile module, and an orifice shaping module. 
     The output characteristic may be a flow rate  114  through the valve  108 , a torque, an engine speed, and/or other output characteristic affected by the opening and the closing of the valve  108 . In one embodiment of the system  100 , the specified relationship may comprise a linear relationship between the valve position and the output characteristic such that for every x degrees of a turn of the valve a y change in the output characteristic occurs. For example, the output characteristic may comprise a portion of a torque-speed map for an engine  102 , where for every x degrees of a turn of the valve  108  an approximately linear y change in the torque-speed is achieved. 
       FIG. 2A  is an illustration depicting one example of a typical or known valve orifice profile  202 . The shape of orifices in most valves is determined by convention and convenience with shapes such as rectangles being prevalent as they are easier to machine. In embodiments comprising typical valve orifice profiles  202 , designers of systems requiring substantially precise monitoring of flows must devote time and expense to testing these orifices profiles  202  and compiling complex piecemeal algorithms. 
       FIG. 2B  is an illustration depicting one embodiment of a shaped valve orifice  204  according to the present disclosure. The shaped valve orifice  204  may comprise an ‘ideal’ shape for a valve orifice such that the shape conforms to a derived shape generated by the orifice shaping module. 
     The derived shape may be utilized in one application, while a best-fit shape may be preferred in an alternate application. The best-fit shape may comprise a shape that may be easier and less costly to produce. The best-fit shape may be derived from a plurality of easily machined shapes. The best-fit shape may be further optimized through an iterative process of testing the best-fit against the desired output.  FIG. 2C  is an illustration depicting one example of a best-fit valve orifice  206 . The best-fit valve orifice  206  may comprise a series of connected straight lines, etching out an area and shape approximating the shaped valve orifice  204  of  FIG. 2B . This configuration may be the easily machined, cost-effective implementation of shaped valve orifice  204 . 
       FIG. 2D  is an illustration depicting an alternate example of a shaped valve orifice  208 . In one embodiment, the shaped valve orifice  208  has an ‘ideal’ shape for a valve orifice such that the shape conforms to a derived shape generated by the orifice shaping module. In one embodiment, the shaped valve orifice  208  has an equivalent effective flow area (EFA) solution as the shaped valve orifice  204 , with the shaped valve orifice  204  comprising a symmetrical embodiment of shaped valve orifice  208 . 
       FIG. 2E  is an illustration depicting one example of a best-fit triangle valve orifice  210 . The best-fit triangle valve orifice  210  may provide a cost-effective implementation of the shaped valve orifice  204 . Iterative testing of the best-fit triangle valve orifice  210  shape may be used to maximize the desired output characteristic. 
       FIG. 2F  is an illustration depicting an alternate example of a best-fit triangle valve orifice  212 . The best-fit triangle valve orifice  212  may provide a cost-effective implementation of the shaped valve orifice  208 . Iterative testing of the best-fit triangle valve orifice  212  shape may be used to maximize the desired output characteristic. 
       FIG. 3A  is a graph illustrating one embodiment of a torque-speed map  300 A for an expected engine duty cycle with an orifice profile corresponding to the typical valve orifice profile  202 . The torque-speed map  300 A depicts a maximum-rated torque line  302 , a high-usage area  304 , a low-usage area  306 , and valve position curves corresponding to 0% valve open curve  308 , 10% valve open curve  310 , 30% valve open curve  312 , 60% valve open curve  314 , and 100% valve open curve  316 . A portion of the torque-speed map  300 A lies below the 0% valve open curve  308 , where there may be no requirement for an open valve. Of the torque-speed workspace portion above the 0% valve open curve  308  about one half of the workspace lies between the 0% valve open curve  308  and the 10% valve open curve  310 . The shape of the typical valve orifice  202  may abruptly permit a significant portion of the total fluid flow through the valve  108  within the first 10% of a total valve rotation. 
       FIG. 3B  is a graph illustrating one embodiment of a torque-speed map  300 B for an expected engine duty cycle with a shaped valve orifice profile, such as one of the profiles corresponding to the shaped orifices shown in  FIGS. 2B-2F . More specifically.  FIG. 3B  may show the torque-speed map  300 B for a reshaped valve orifice  204  from  FIG. 2B . In one embodiment,  FIG. 3B  comprises a linearization of the function consisting of the valve position versus torque-speed. For example, at an initial 10% open turn of the shaped valve  108 , with a shaped value orifice, a corresponding 10% increase in torque-speed is achieved versus a valve  108  with a typical valve orifice shape. In the map  300 A associated with a typical valve orifice shape, the open valve curve at 10% corresponds to nearly 50% of the torque-speed. 
       FIG. 4A  is a graph illustrating one embodiment of a torque-speed map  400 A for an expected engine duty cycle with a typical valve orifice  202 . The torque-speed map  400 A may be for an over-the-road tractor trailer where the high-usage area of the torque-speed map  400  occurs in region  402  where the tractor maintains a constant speed for much of the operation cycle, and region  404  where the tractor may idle.  FIG. 4A  shows the valve open percentage for a typical valve orifice  202 , where much of the torque-speed map  400  lies under the 10% valve open curve  310 . 
       FIG. 4B  is a graph illustrating one embodiment of a torque-speed map  400 B for an expected engine duty cycle with a shaped valve orifice profile associated with one of the shaped orifices of  FIGS. 2B-2F . In one embodiment, the relationship between the percentage of the valve  108  open and the percentage of the torque-speed workspace utilized comprises a linear relationship. 
       FIG. 5A  is a graph illustrating one embodiment of a torque-speed workspace area histogram  500 A for a valve position of a shaped valve  108  with a shaped valve orifice according to at least one of the embodiments disclosed herein. In one embodiment, the area histogram  500 A corresponds to the torque-speed workspace map  400 B and provides an additional manner of analyzing the data of the torque-speed workspace map  400 B. The histogram  500 A may be used to identify points along the torque-speed workspace map  400 B to facilitate calibration of the shaped valve orifice. 
       FIG. 5B  is a graph illustrating one embodiment of a high resolution torque-speed workspace area histogram  500 B. In one example, the high resolution torque-speed workspace area histogram  500 B comprises the workspace area histogram of  FIG. 5A  in greater detail. The higher resolution of  FIG. 5B  may be utilized to yield a more precisely calibrated valve orifice shape. 
       FIG. 6  is a graph illustrating one embodiment of a torque-speed workspace cumulative usage  600  for a valve position of a shaped valve  108  according to the present disclosure. The graph of cumulative usage  600  may comprise an example of cumulative usage for the torque-speed workspace histograms  500 A,  500 B. The torque-speed workspace cumulative usage  600  shows the large initial increase in workspace usage within the first 10% of an open valve with decreasing additional workspace usage occurring over the succeeding intervals. 
       FIG. 7  is a graph illustrating an alternate embodiment of a high resolution torque-speed workspace area histogram  700  for a valve position of a shaped valve  108 . The high resolution torque-speed workspace area histogram  700  may comprise an example of a more precise rendering of the torque-speed workspace area histograms  500 A,  500 B. The more precise rendering may allow for a more accurate shaping of the shaped valve orifice. 
       FIG. 8  is a graph illustrating an example of a high resolution torque-speed workspace cumulative usage  800  for a valve position of a shaped valve  108 . The high resolution torque-speed workspace cumulative usage  800  may comprise an example of the cumulative usage  800  of the high resolution torque-speed workspace area histogram  700 . 
       FIG. 9  is a table illustrating one embodiment of required inputs  900  for optimizing an orifice shape. The required inputs  900  may comprise inputs to a function used to map geometric coordinates from a typical valve orifice to a reshaped valve orifice for a particular application. For example, for each specified point along the cumulative histogram  800 , the output characteristic of a current effective flow area (EFA)  904  may be translated by an adjustment factor to a desired EFA  908 , and a corresponding current θ position  902  of a valve  108  may be translated by an adjustment factor to a desired θ position  906  of the valve  108 . 
       FIG. 10  is an illustration depicting one embodiment of a closed valve geometry  1000  of a shaped valve  108 . The closed valve geometry  1000  illustration shows an exhaust gas  1002  directed toward the valve, a radius  1004 , a y-axis  1006 , a z-axis  1008 , and a width  1010  (w 0 ). An x-axis (not shown) perpendicularly pierces the y-z intersection. 
       FIG. 11  is an illustration depicting one embodiment of a partially open valve geometry  1100 . The partially open valve geometry  1100  illustration shows the exhaust gas  1002 , the radius  1004 , the y-axis  1006 , the z-axis  1008 , the w 0    1010 , a width  1012  (w 1 ), a width  1014  (w 2 ), and an angle  1016  (α). 
       FIG. 12  is a graph illustrating one embodiment of a reshaping map  1200  of a typical valve orifice  202 . The reshaping map  1200  shows an original conventional valve orifice profile  1202 , a reshaped valve orifice profile  1204 , the x-axis  1206 , and the y-axis  1208 . In one embodiment, the reshaping map  1200  may be derived by using a projected exposed area (PEA) as an approximation of an effective flow area (EFA) in conjunction with the histograms of  FIGS. 7 and 8 , and the valve geometries shown in  FIGS. 10 and 11 . 
     For example, a current shaped valve  108  comprises a typical valve orifice  202  but modified according to the workspace area percent usage for the plurality of valve positions as shown in  FIG. 7 . The histogram  700  of  FIG. 7  is translated into the cumulative percent usage  800  for the valve position as shown in  FIG. 8 . Referring to  FIGS. 10 and 11 , the current or reshaped orifice profile (COF) may be defined as a function of the y-axis such that COF=f(y). An angle θ may be defined such that θ=α·π/4. The width w 0  may be written as w 0 =r√{square root over (2)}, width w 1  may be written as w 1 =r*cos(π/4)−r*cos(π/4+θ), and width W, may be written as w 2 =w 1 /sin θ. An exposed area (A) may be written as A=2∫f(y)dy integrated over the interval w 0 /2 to w 0 /2−w 2 . The projected exposed area (PEA) may now be written as PEA=A sin θ. 
     In the continuing example, a desired percentage of valve rotation (θ) may be described as a function of the cumulative workspace histogram  800  such that θ=h c (θ) where h c  represents the cumulative workspace usage histogram of  FIG. 8  and θ represents a current valve open position. By incorporating the desired theta (θ) into the PEA definition a desired area may be circumscribed: PEA=A sin θ=A sin θ, therefore A=A(sin θ/sin θ). Other features of the desired valve profile may be derived where w 0 =w 0 =r cos(π/4)−r cos(π/4+θ), and w 2 =w 1 /sin θ. Increments of change for the shaping of the desired valve profile for each slice of the histogram may be achieved using the following formulas where k comprises an incremental counter for each slice of the histogram: θ k+1 =θ k +Δθ, A k+1 =A k +ΔA, Δy=w 2     k+1   −w 2     ,   , and x k+1 *Δy=ΔA. 
     The schematic flow chart diagrams that follow are generally set forth as logical flow chart diagrams. As such, the depicted order and labeled steps are indicative of one embodiment of the presented method. Other steps and methods may be conceived that are equivalent in function, logic, or effect to one or more steps, or portions thereof, of the illustrated method. Additionally, the format and symbols employed are provided to explain the logical steps of the method and are understood not to limit the scope of the method. Although various arrow types and line types may be employed in the flow chart diagrams, they are understood not to limit the scope of the corresponding method. Indeed, some arrows or other connectors may be used to indicate only the logical flow of the method. For instance, an arrow may indicate a waiting or monitoring period of unspecified duration between enumerated steps of the depicted method. Additionally, the order in which a particular method occurs may or may not strictly adhere to the order of the corresponding steps shown. 
       FIG. 13  is a schematic block diagram depicting one embodiment of a method  1300  for shaping a valve orifice. The method  1300  includes determining  1302  a specified relationship between a valve position and an output characteristic, such as valve flow and torque-speed. The method  1300  further includes determining  1304  an orifice profile from a calibration valve. At  1306 , a determination is made whether the output characteristic is valve flow or torque-speed map usage. If the output characteristic is valve flow, then the method  1300  continues by shaping  1308  the orifice according to the linear relationship between valve position and valve flow. If the output characteristic is torque-speed, then the method  1300  continues by shaping  1308  the orifice according to linear relationship between valve position and a torque-speed map usage. After the orifice shape is determined, the method  1300  includes determining  1312  if the orifice shape is physically realizable. If it is determined that the orifice shape is physically realizable, then the method  1300  ends. If, however, it is determined that the orifice shape is not physically realizable, then the method  1300  continues by shaping  1314  the orifice to the closest physically realizable shape. 
     Referring to  FIG. 14 , a method  1400  for shaping a valve orifice includes determining  1302  a specified relationship between a valve position and an output characteristic. The method  1400  also includes determining  1304  an orifice profile based at least partially on the specified relationship. A desired shaping method is then selected at  1402 . In some embodiments, the selected desired shaping method is either a triangle shaping method or a method based on easily-machined (EM) shapes. If the triangle shaping method is selected at  1402 , then the method  1400  continues to shape an orifice to a best triangular approximation of the orifice profile. If, however, the EM shaping method  1400  is selected at  1402 , then the method  1400  continues to shape the orifice to the closest EM shape. Following shaping of the orifice, the method  1400  ends. 
     Referring now to  FIG. 15 , a method  1500  for shaping a valve orifice includes determining  1502  a specified relationship between a valve position and an output characteristic. The method  1500  also includes determining  1504  a first orifice profile based at least partially on the specified relationship. The method  1500  proceeds with shaping  1506  a first orifice based at least partially on the specified relationship and first orifice profile. Additionally, the method  1500  includes determining  1508  a performance curve for the first orifice and determining  1510  an improvement index for the first orifice. The method  1500  further includes generating a second orifice profile based on the improvement index and the first orifice profile and shaping  1514  a second orifice based at least partially on the second orifice profile. 
     The various actions of the methods described herein can be performed by any of various modules or sub-modules forming part of one or more apparatus, systems, or devices, or being in a stand-alone configuration. For example, the disclosure contemplates the use of an apparatus that has a specified relationship module, an orifice profile module, and an orifice shaping module each configured to perform specific actions for optimizing an orifice shape. 
     The present invention may be embodied in other specific forms without departing from its spirit or essential characteristics. The described embodiments are to be considered in all respects only as illustrative and not restrictive. The scope of the invention is, therefore, indicated by the appended claims rather than by the foregoing description. All changes which come within the meaning and range of equivalency of the claims are to be embraced within their scope.