Patent Publication Number: US-10760592-B1

Title: Gas turbine engine airfoil frequency design

Description:
CROSS-REFERENCE TO RELATED APPLICATIONS 
     This disclosure claims priority to U.S. Provisional Patent Application No. 62/446,908 filed Jan. 17, 2017. 
    
    
     BACKGROUND 
     The disclosure relates to turbomachinery. More particularly, the disclosure relates to gas turbine engine airfoils and their designed vibrational responses. 
     Airfoils of turbine engine blades and vanes are subject to a number of performance-affecting conditions. The airfoils are subject to environmental exposure and thermal and mechanical loading. These factors are significant in each section of the engine for a variety of reasons. For example, in the fan section of high bypass engines, the airfoils have a large diameter with a relatively small thickness. In a high pressure compressor and in a turbine section, the airfoil is exposed to high temperatures. Cooling passages are provided in the turbine section airfoils, but such cooling passages are typically absent in the compressor section. For blades, rotational forces are also a significant dynamic stimulus. 
     Vibrational responses of the airfoil can provide an indication of how durable the airfoil will be during engine operation. If an airfoil operates too long at a resonant frequency during engine operation, the life of the airfoil may be significantly shortened as the airfoil is more highly stressed. An exemplary vibrational testing method is defined in United States Federal Aviation Administration (FAA) Advisory Circular 38.83-1 (Sep. 8, 2009). Designing airfoils with desirable resonant frequencies can prolong the useful life of engine components, particularly the airfoil itself. 
     SUMMARY 
     In one exemplary embodiment, a turbomachine airfoil element includes an airfoil that has pressure and suction sides spaced apart from one another in a thickness direction and joined to one another at leading and trailing edges. The airfoil extends in a radial direction a span that is in a range of 17.2-18.2 inches (436-462 mm). A chord length extends in a chordwise direction from the leading edge to the trailing edge at 50% span is in a range of 10.0-11.0 inches (255-281 mm). The airfoil element includes at least two of a first mode with a frequency of 51±10% Hz, a second mode with a frequency of 147±10% Hz, a third mode with a frequency of 267±10% Hz, a fourth mode with a frequency of 350±10% Hz, a fifth mode with a frequency of 454±10% Hz and a sixth mode with a frequency of 619±10% Hz. 
     In a further embodiment of the above, three of the first, second, third and fifth mode frequencies are present. 
     In a further embodiment of any of the above, the first mode is a 1EB mode. The second mode is a 2EB mode and the third mode is a 1T mode. 
     In a further embodiment of any of the above, the 1EB and 2EB modes correspond to deflections substantially parallel to thickness direction. The 1T mode corresponds to twisting about the radial direction. 
     In a further embodiment of any of the above, the frequencies are at zero speed and ambient conditions. 
     In a further embodiment of any of the above, at a running speed/condition, the first mode has a frequency of 95±10% Hz, the second mode has a frequency of 222±10% Hz, the third mode has a frequency of 288±10% Hz, the fourth mode has a frequency of 394±10% Hz, the fifth mode has a frequency of 524±10% Hz and the sixth mode has a frequency of 682±10% Hz. 
     In a further embodiment of any of the above, the frequencies are within ±5% ranges. 
     In a further embodiment of any of the above, the airfoil element is part of a blade. 
     In a further embodiment of any of the above, the is a titanium-based airfoil alloy. 
     In a further embodiment of any of the above, the titanium-based alloy has a density of about 0.16 lb/in 3  (4.4 g/cm 3 ). 
     In a further embodiment of any of the above, the titanium-based alloy has a modulus of elasticity of about 16-17 Mpsi (110-117 GPa) at room temperature. 
     In another exemplary embodiment, a method of repairing an airfoil comprising the steps of providing an airfoil that has pressure and suction sides spaced apart from one another in a thickness direction and joined to one another at leading and trailing edges. The airfoil extends in a radial direction a span that is in a range of 17.2-18.2 inches (436-462 mm). A chord length extends in a chordwise direction from the leading edge to the trailing edge at 50% span and is in a range of 10.0-11.0 inches (255-281 mm). The provided airfoil has at least one unrestored mode frequency that is attributable to damage to the airfoil. The airfoil is repaired to provide at least two of a first mode has a frequency of 51±10% Hz, a second mode has a frequency of 147±10% Hz, a third mode has a frequency of 267±10% Hz, a fourth mode has a frequency of 350±10% Hz, a fifth mode has a frequency of 454±10% Hz and a sixth mode has a frequency of 619±10% Hz. At least one of the first mode frequency, second mode frequency, third mode frequency, fourth mode frequency, fifth mode frequency, and sixth mode resonance frequency corresponds to a restored mode resonance frequency that supersedes the unrestored mode frequency. 
     In a further embodiment of any of the above, the first mode is a 1EB mode. The second mode is a 2EB mode and the third mode is a 1T mode. The frequencies are at zero speed and ambient conditions. The airfoil is a titanium-based alloy. 
     In another exemplary embodiment, a turbofan engine includes a fan section and a compressor section arranged fluidly downstream from the fan section. A turbine section is arranged fluidly downstream from the compressor section. A combustor is arranged fluidly between the compressor and turbine sections. An airfoil in at least one of the fan, compressor and turbine sections. The airfoil has pressure and suction sides spaced apart from one another in a thickness direction and joined to one another at leading and trailing edges. The airfoil extends in a radial direction a span that is in a range of 17.2-18.2 inches (436-462 mm). A chord length extends in a chordwise direction from the leading edge to the trailing edge at 50% span and is in a range of 10.0-11.0 inches (255-281 mm). At least two of a first mode has a frequency of 51±10% Hz. A second mode has a frequency of 147±10% Hz. A third mode has a frequency of 267±10% Hz. A fourth mode has a frequency of 350±10% Hz. A fifth mode has a frequency of 454±10% Hz and a sixth mode has a frequency of 619±10% Hz. 
     In a further embodiment of any of the above, the airfoil is provided in the fan section. 
     In a further embodiment of any of the above, the airfoil element is part of a blade. 
     In a further embodiment of any of the above, the airfoil is an titanium-based alloy with a density of about 0.16 lb/in 3  (4.4 g/cm 3 ) and with a modulus of elasticity of about 16-17 Mpsi (110-117 GPa) at room temperature. 
     In a further embodiment of any of the above, the frequencies are at zero speed and ambient conditions. 
     In a further embodiment of any of the above, the first mode is a 1EB mode, the second mode is a 2EB mode, and the third mode is a 1T mode. 
     In a further embodiment of any of the above, the 1EB and 2EB modes correspond to deflections substantially parallel to thickness direction. The 1T mode corresponds to twisting about the radial direction. 
    
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
       The disclosure can be further understood by reference to the following detailed description when considered in connection with the accompanying drawings wherein: 
         FIG. 1A  is a view of a perspective view of an example airfoil element. 
         FIG. 1B  is top view of the airfoil of  FIG. 1A . 
         FIG. 2  is a schematic sectional view of a fan section, a low pressure compressor and a high pressure compressor of an example turbofan engine. 
         FIG. 3  is a schematic perspective view of an example fan blade and a portion of a fan hub. 
         FIG. 4A  is a schematic perspective view of an integrally bladed rotor. 
         FIG. 4B  is a schematic perspective view of a compressor blade airfoil with a root. 
         FIG. 5A  is a schematic side view of a cantilevered stator vane. 
         FIG. 5B  is a schematic side view of a stator vane with an inner diameter shroud. 
         FIG. 5C  is a schematic side view of an adjustable inlet guide vane. 
         FIG. 6A  is a schematic side view of an airfoil showing a first easywise bending mode node line. 
         FIG. 6B  is an inward view of the airfoil of  FIG. 6A  with one vibrational extreme shown in broken lines. 
         FIG. 6C  is a front view of the airfoil of  FIG. 6A  with both vibrational extremes shown in broken lines. 
         FIG. 6D  is a front view of an airfoil with second easywise bending mode extremes shown in broken lines. 
         FIG. 6E  is a front view of an airfoil with third easywise bending mode extremes shown in broken lines. 
         FIG. 7A  is a side view of an airfoil showing a torsion mode node line. 
         FIG. 7B  is an inward view of the airfoil of  FIG. 7A , with one torsional extreme shown in broken lines. 
         FIG. 8A  is a side view of an airfoil showing a first stiffwise bending mode node line. 
         FIG. 8B  is an inward view of the airfoil of  FIG. 8A  with a rearward vibrational extreme shown in broken lines. 
         FIG. 9A  is a front view of a circumferential array of stator vanes. 
         FIG. 9B  is a side view of the array of  FIG. 9A  with an axial vibrational extreme shown in broken lines. 
         FIG. 10  is a Campbell diagram of an airfoil. 
         FIG. 11  is a schematic sectional view of a turbofan engine. 
     
    
    
     The embodiments, examples and alternatives of the preceding paragraphs, the claims, or the following description and drawings, including any of their various aspects or respective individual features, may be taken independently or in any combination. Features described in connection with one embodiment are applicable to all embodiments, unless such features are incompatible. Like reference numbers and designations in the various drawings indicate like elements. 
     DETAILED DESCRIPTION 
       FIG. 11  schematically illustrates a gas turbine engine  320 . The exemplary gas turbine engine  320  is a two-spool turbofan engine that generally incorporates a fan section  322 , a compressor section  324 , a combustor section  326  and a turbine section  328 . Alternative engines might include an augmenter section (not shown) among other systems or features. The fan section  322  drives an inlet airflow to split with a bypass portion being driven along an outboard bypass flow path, while the core portion is further driven by a compressor section  324  along a core flow path for compression and communication into the combustor section  326 . The hot combustion gases generated in the combustor section  326  are expanded through the turbine section  328 . Although depicted as a turbofan gas turbine engine in the disclosed non-limiting embodiment, it should be understood that the concepts described herein are not limited to turbofan engines and these teachings could extend to other types of engines, including but not limited to, geared turbine engines having a geared architecture  348 , three-spool engine architectures, and ground-based engines. 
     The exemplary fan section comprises a fan case  335  surrounding a fan  340  which comprises a circumferential array of fan blades  342 . In the exemplary two-spool engine, the low pressure spool  330  comprises a shaft  331  rotatable about axis A joining a first (or low) pressure compressor (LPC) section  338  to a first (or low) pressure turbine (LPT) section  339 . Similarly, a second (or high) speed spool  332  comprises a shaft  333  rotatable about axis A coupling a second (or high) pressure compressor section  352  to the high pressure turbine section  354 . 
     The core airflow is compressed by the low pressure compressor  338  then the high pressure compressor  352 , mixed and burned with fuel in the combustor  326 , then expanded over the high pressure turbine  354  and low pressure turbine  339 . The turbines  354 ,  339  rotationally drive the respective low speed spool  330  and high speed spool  332  in response to the expansion. It will be appreciated that each of the positions of the fan section  322 , compressor section  324 , combustor section  326 , turbine section  328 , and fan drive gear system  348  may be varied. For example, gear system  348  may be located aft of combustor section  326  or even aft of turbine section  328 , and fan section  322  may be positioned forward or aft of the location of gear system  348 . 
     In a non-limiting embodiment, the  FIG. 11  gas turbine engine  320  is a high-bypass geared aircraft engine. In a further example, the gas turbine engine  320  bypass ratio is greater than about six (6:1). The geared architecture  348  can include an epicyclic gear train, such as a planetary gear system or other gear system. The example epicyclic gear train has a gear reduction ratio of greater than about 2.3:1, and in another example is greater than about 2.5:1. The exemplary geared architecture transmits driving torque from the low pressure spool to the fan with a geared reduction. The geared turbofan enables operation of the low speed spool  330  at higher speeds, which can increase the operational efficiency of the low pressure compressor  338  and low pressure turbine  339  and render increased pressure in a fewer number of stages. It should be understood, however, that the above parameters are only exemplary of one embodiment of a geared architecture engine and that the present invention is applicable to other gas turbine engines including direct drive turbofans. 
     In one non-limiting embodiment, the bypass ratio of the gas turbine engine  320  is greater than about ten (10:1), the fan diameter is significantly larger than that of the low pressure compressor  338 , and the low pressure turbine  339  has a pressure ratio that is greater than about five (5:1). Low pressure turbine pressure ratio is pressure measured prior to inlet of low pressure turbine  339  as related to the pressure at the outlet of the low pressure turbine  339  prior to an exhaust nozzle. It should be understood, however, that the above parameters are only exemplary of one embodiment of a geared architecture engine and that the present disclosure is applicable to other gas turbine engines, including direct drive turbofans. 
     In this embodiment of the exemplary gas turbine engine  320 , a significant amount of thrust is provided by the bypass flow path B due to the high bypass ratio. The fan section  322  of the gas turbine engine  320  is designed for a particular flight condition—typically cruise at about 0.8 Mach and about 35,000 feet. This flight condition, with the gas turbine engine  320  at its best fuel consumption, is also known as bucket cruise thrust specific fuel consumption (TSFC). TSFC is an industry standard parameter of fuel consumption per unit of thrust the engine produces at that minimum point. 
     Fan pressure ratio (FPR) is the pressure ratio across an airfoil of the fan section  322  without the use of a fan exit guide vane (FEGV) system. The low fan pressure ratio according to one non-limiting embodiment of the example gas turbine engine  320  is less than 1.45. Low corrected fan tip speed (LCFTS) is the actual fan tip speed divided by an industry standard temperature correction of [(Tram ° R)/(518.7° R)] 0.5 . The low corrected fan tip speed according to one non-limiting embodiment of the example gas turbine engine  320  is less than about 1150 fps (350 m/s). 
     Airfoils are used throughout the fan, compressor and turbine sections  340 ,  338 ,  328  within the bypass and core flow paths. The airfoils can be supported relative to the engine static structure  336  or spools using a variety of techniques. Turning now to  FIGS. 1A-1B , an engine airfoil element  20 , for example, a blade or a vane, extends in a radial direction R, or spanwise, from at least one flow path surface  22 , for example, a platform or a shroud, to, for example, a tip  24  or a shroud. The airfoil element  20  includes an airfoil  21  having leading and trailing edges  26 ,  28  spaced apart in a chord-wise direction H. In the case of a blade, the tip  24  is arranged adjacent to a blade outer air seal. 
     The airfoil  21  includes pressure (typically concave) and suction (typically convex) sides  30 ,  32  spaced apart in an airfoil thickness direction T, generally perpendicular to the chord-wise direction H, that are joined at the leading and trailing edges  26 ,  28 . Multiple airfoils  21  are arranged circumferentially in a circumferential direction C in an array. 
     As shown in  FIG. 1A , the airfoil  20  has a radial span R S  and a chord length L C . An inner or outer platform or a shroud may be provided at one or both radial extremities of the airfoil  20 , depending upon the application (see, e.g.,  FIGS. 3-5C ). R S  may be defined as the minimum radial distance between the radially outboard-most portion of airfoil  20 , which may be the tip  24  in the case of a blade, to the radially inboard-most portion of the airfoil  20 . The radially inboard- or outboard most portion may be an end supported by elastomeric potting material and an inner or outer ring, or a vane having an integral inner or outer shroud. Alternatively, both ends of the airfoil may be supported in radially spaced rings by potting. R S  may be defined as excluding any fillet that adjoins the airfoil&#39;s aerodynamic exterior surface to any inner or outer platform or shroud. L C  may be defined as the distance from the leading edge  26  to the trailing edge  28  at about 50% span. For example, R S  is 17.2-18.2 inches (436-462 mm) and L C  is 10.0-11.0 inches (255-281 mm). In one example, the airfoils  20  in the array may be configured to provide an asymmetry to reduce undesired vibrations, for example, by arranging airfoils slightly different geometries in a circumferentially alternating pattern. In one example, first and second sets of airfoils are interleaved with one set of airfoils having an L C  that is less the L C  of the other set of airfoils by 0.001 inch (0.03 mm) or less. 
       FIG. 2  schematically illustrates one example fan section  340  and compressor section  324  in more detail. An array of fan exit stator (FES)  341  are provided at an inlet of the core flow path downstream from the fan  342 . Variable inlet guide vanes (IGV)  343 , adjustable using actuators  345 , are arranged fluidly between the FESs  341  and the LPC  338 . In the disclosed example, the LPC  338  has three stages of alternating arrays of rotating blades ( 338   a ,  338   c ,  338   e ) and fixed stator vanes ( 338   b ,  338   d ,  338   f ), and the HPC  352  has eight stages of alternating arrays of rotating blades ( 352   a ,  352   c ,  352   e ,  352   g ,  352   i ,  352   k ,  352   m ,  352   o ) and fixed stator vanes ( 352   b ,  352   d ,  352   f ,  352   h ,  352   j ,  352   l ,  352   n ,  352   p ). A different number of stages or a different configuration of blades and vanes can be used if desired. In one example, the disclosed airfoil&#39;s resonant frequency is designed for the fan  342 . 
     The fan blades  342  include roots (not shown) that are received in a slotted hub  337  ( FIG. 3 ). In the example compressor section  324 , the blades in the LPC  338  and HPC  352  are integrally bladed rotors ( FIG. 4A ) in which the airfoils are integrally formed with the rotor as a unitary structure, rather than rooted blades ( FIG. 4B ) that are received in correspondingly shaped slots in a rotor. The stator vanes in the compressor section  324  are cantilevered ( FIG. 5A ) such that each airfoil extends radially inward from an outer shroud  360  supported by an outer case  362  to a tip  364  that is supported by a potting material within an inner diameter ring (not shown). The eighth stage HPC stator  352   p  may be a “ringed” stator (e.g., “ring-strut-ring”;  FIGS. 5B and 9A-9B ) array in which an inner shroud  366  also is provided at an inner diameter of the airfoils, to be joined to one another. The IGV  343  is pivotally supported by the inner and outer shrouds  360 ,  366  for rotation about a generally radially oriented axis  368  ( FIG. 5C ). 
     The airfoil may be formed using any suitable process, for example, casting, forging and/or machining. Any suitable material can be used to provide the airfoil and may be determined based upon factors such as airfoil stresses, engine operating speeds, gas flow dynamics and operating temperatures. In one example, airfoils in the fan section are constructed from an aluminum-based alloy, airfoils in the low pressure compressor section are constructed from an aluminum-based alloy, and airfoils in the high pressure compressor section are constructed from a nickel-based superalloy. One example aluminum-based alloy is 7075 with a density of about 0.103 lb/in 3  (2.85 g/cm 3 ) and a modulus of elasticity of about 10.4 Mpsi (71 GPa) at room temperature. One example titanium-based alloy is Ti-6Al-4V, which has a density of about 0.16 lb/in 3  (4.4 g/cm 3 ) and a modulus of elasticity of about 16-17 Mpsi (110-117 GPa) at room temperature. Example nickel-based superalloys are Inconel 718 and ME  16 . These nickel-based superalloys have a density of approximately 0.3 lb/in 3  (8.3 g/cm 3 ), and more broadly 0.28-0.32 lb/in 3  (7.7-8.9 g/cm 3 ). In addition, the nickel-based superalloy material has a modulus of elasticity of approximately 30 Mpsi (206 GPa), and more broadly 27-36 Mpsi (186-248 GPa) at room temperature. The airfoils may also have a coating system. 
     A resonant condition is where a frequency of the excitation coincides with a frequency of the airfoil, and may result in high vibratory stress. The airfoil has a number of frequencies that can be resonant at various speeds. There are various modes of vibration, each with its associated natural frequency. As for airfoils, generally six vibratory modes primarily reflect how the airfoils interact with each other, and with other components of the engine. The type (EB, T, SWB, CWB, ND) and number (1, 2, 3, etc.) of the various modes may be ordered interchangeably through this disclosure (e.g., 1EB is the same as EB1). 
     A first type of mode is easywise bending (EB). An airfoil can be approximated as a cantilevered beam extending in the radial direction for the engine. The easywise bending is parallel to the shortest dimension, or in the thickness direction T. 
       FIGS. 6A-6E  illustrate various easywise bending modes.  FIG. 6B  shows bi-directional movement in the direction  520  with a neutral condition that is, without deflection, shown in solid lines.  FIG. 6B  also shows one of two extremes, that is, with relatively extreme deflection in broken lines.  FIG. 6A  is a plan view of the airfoil, illustrating node line  522 , which is the location of each node in cross sections of the airfoil having deflections illustrated in  FIG. 6C .  FIG. 6C  shows both extremes of EB1 (1EB) movement in broken lines. A first EB mode (EB1 or 1EB;  FIG. 6C ) is the EB mode of lowest frequency. A second EB mode (2EB or EB2;  FIG. 6D ) deflection, is a mode that encompasses two node lines  522 A and  522 B. The mode has one portion of the airfoil moving toward the pressure side and another toward the suction side, changing direction for each cycle of vibration. Note there is no corresponding plan view illustrating the node lines  522 A and  522 B, though the locations of the two horizontal node lines relative to the airfoil height is readily apparent. EB3 or 3EB ( FIG. 6E ) is a further EB mode and illustrates three node lines  522 A,  522 B, and  522 C. Other EB modes may exist, and the mode number is indicated by the numeral following “EB.” 
     The twist or torsion (T) modes ( FIGS. 7A and 7B ) involve bi-directional twist in direction  540  twist generally about a spanwise axis for the airfoil, which is a radial axis from the center of the airfoil, or node line  542 . As with  FIG. 6B , one torsional extreme is shown in broken lines with the neutral, deflection free condition shown in solid lines as shown in  FIG. 7B . As with EB and other modes, there are a series of torsion modes, including 1T (T1), 2T (T2), etc. 
     The stiffwise bending (SWB) modes ( FIGS. 8A and 8B ) are generally normal to the EB modes in the chordwise direction H such that the corners of the airfoil tip at the leading and trailing edges remain in-plane. The SWB resonance frequencies will be higher than the corresponding EB resonance frequencies. As with  FIG. 6B ,  FIG. 8B  shows bi-directional movement in a direction  530  with one extreme (a trailing-edge shifted extreme) shown in broken lines relative to a solid line neutral position. The node line is shown as  532 . As with EB and other modes, there are a series of stiffwise bending modes, including 1SWB (SWB1), 2SWB (SWB2), etc. 
     There are other modes as well. The chordwise bending (CWB) mode are where the corners of the airfoil tip at the leading and trailing edges vibrate out-of-plane in the same direction at the same time. As with EB and other modes, there are a series of chordwise bending modes, including 1CWB (CWB1), 2CWB (CWB2), etc. Trailing edge bending (TEB) modes are bending modes that bend primarily along the trailing edge, and leading edge bending (LEB) modes are bending modes that bend primarily along the leading edge. Some modes may be a more complex combination of bending and torsion such that the complex mode (M) cannot be characterized as one mode. In another example, a nodal diameter (ND) bending mode ( FIGS. 9A and 9B ) has movement in an axial direction. Since one of the inner and outer platforms  360 ,  362  of the stator vanes are fixed to the outer case  362 , the joined inner shrouds  366  can vibrate in unison axially forward and aft in a zero nodal diameter (ND0 or 0ND). Another type of nodal diameter is referred to as an aliased nodal diameter, which corresponds to the upstream blade count minus the stator count of the stage in question. In one example, for a stage with  117  stator vanes with sixty-six upstream blades in the adjacent stage, the aliased nodal diameter is fifty-one (ND51 or 51ND). In this aliased nodal diameter, there is are fifty-one peaks/troughs vibrating in the radial direction at each of the inner and outer diameters of the stator stage. In the case of stator vanes, where the presence of the shroud has a significant impact on the vibrational mode, the mode in Table 1 also includes the designation —SH. As a general matter, however, the lowest resonance frequency is expected to be that of the EB1 mode. The remaining details of airfoil configuration may influence the relative positioning of the remaining modes. 
     Table I below and  FIG. 10  provide parameters of the particular resonance profile: 
     
       
         
           
               
               
               
               
             
               
                 TABLE I 
               
               
                   
               
               
                   
                   
                 Min Cruise 
                 Redline  
               
               
                   
                 Zero Speed 
                 Nominal Freq. 
                 Nominal Freq. 
               
               
                   
                 Nominal  
                 (Hz) @ speed 
                 (Hz) @ speed 
               
               
                 Mode 
                 Freq. (Hz) 
                 range (rpm) 
                 range (rpm) 
               
               
                   
               
             
            
               
                   
               
            
           
           
               
               
               
               
            
               
                 lEB 
                 51 
                 95 
                 104 
               
               
                 2EB 
                 147 
                 222 
                 240 
               
               
                 1T 
                 267 
                 288 
                 291 
               
               
                 M4 
                 350 
                 394 
                 398 
               
               
                 M5 
                 454 
                 524 
                 545 
               
               
                 M6 
                 619 
                 682 
                 685 
               
               
                   
               
            
           
         
       
     
     The above frequencies relate primarily to the airfoils. The frequencies also include the effects of a root, platform, rim, disk and/or rotor. In the case of a stator vane, where the effects of the shroud have an appreciable effect, “—SH” is indicated under “Mode” in the tables. In the case of an array with an asymmetrical arrangement of airfoils, the above frequencies represent an average of the frequencies of the different airfoils. Tolerance for the nominal frequencies around these nominal values at each of these speeds is ±10%, more narrowly, ±5%. Exemplary zero speed frequencies are at ambient conditions (e.g., 20-28° C.). For the engine using this airfoil element, exemplary running speeds for the fan  342  are: idle speed is 1000-1200 rpm; min. cruise speed is 4200-4700 rpm; and redline speed is 5000-5600 rpm. 
     While frequencies are a function of the airfoil length, stiffness, and mass, they also represent the unique design characteristic of the airfoil. During the airfoil design, the resonance frequencies may be modified by selective modification of the airfoil root stiffness, length, chord, external thickness, or internal features (such as but not limited to rib location/thickness, or wall thickness, etc.). Any changes to the resonance frequencies could render the airfoil unacceptable for continued operation in the field without high vibratory stresses which can result in high cycle fatigue cracking. One skilled in vibration analysis and design would understand that these resonance frequency characteristics are unique for each airfoil and should account for, for example, the specific operational vibratory environment. The frequencies are determined using computer modelling, for example, ANSYS, although the frequencies may be measured experimentally. 
       FIG. 10  is a Campbell diagram, with frequency and rotational speed on the axes, which plots the resonant frequencies for the airfoil against engine rotor speed. That is, the Campbell diagram illustrates the unique frequency characteristics of the airfoil and captures the vibratory resonance of the airfoil. The modal frequencies change with speed because of the increased temperature (reducing frequency) and centrifugal stiffening (increasing the frequency). The frequencies (which, as indicated, are unique for each airfoil) are represented by essentially horizontal lines  420 ,  422 ,  424 ,  426 ,  428 , and  430 . These illustrate, against the engine rotor speed, the frequency of the 1st easy-wise bending (1EB), 1st stiff-wise bending (SWB), 1st torsion (1T), 2nd easy-wise bending (2EB), 2nd torsion (2T), and 2nd trailing edge bending (2TEB) vibratory modes, or any other modes relevant to the airfoil, for example, summarized in Table I. However, the sequence of the modes or type of mode varies and may be different for each airfoil. The Campbell diagram has angled lines  400 ,  402 ,  404 ,  406 ,  408 ,  410 ,  412 ,  414 , and  416 . These angled lines, called excitation orders, represent the excitation from upstream and downstream stationary airfoils or other interruptions in the flowpath that the airfoil feels as it rotates past the stationary airfoils. 
     For example, lines  400 ,  402 , and  404  may be components of a once per revolution excitation. The airfoils can feel this excitation for excitation orders 1E, 2E, 3E, 4E, and 5E. Lines  400 ,  402 , and  404 , represent 4E, 6E, and 7E, respectively. In any flowpath, there are general aerodynamic disturbances which the airfoils feel at multiples of the rotor spin frequency. 1E is one excitation per revolution or the rotor spin frequency (in cycles per second). The airfoils feel multiples of this once per revolution. 
     As illustrated for the airfoil, the 6E ( 402 ), and 7E ( 404 ) excitation orders are plotted on the Campbell diagram and are a potential concern because there are resonance crossings with the first bending mode (line  420 ) at high speed. The 4E line (line  400 ) does not have a crossing and is of less significance. 
     In addition, lines  410  and  412  respectively are excitation functions that are proportional to the vane counts of the vane stages immediately upstream and downstream of the airfoil stage in question. Lines  414  and  416  are twice  410  and  412  excitations and are relevant to Fourier decomposition of excitations. Lines  406  and  408  are proportional to counts of downstream struts (which are big structural airfoils that are part of the bearing supports; in this example, the strut count is different on two halves of the engine circumference). 
     Where the resonance frequency lines (represented by lines  420 ,  422 ,  424 ,  426 ,  428 , and  430 ) intersect the excitation lines (represented by the angled lines  400 ,  402 ,  404 ,  406 ,  408 ,  410 ,  412 ,  414 , and  416 ) a resonant condition occurs, which, as indicated, may result in high vibratory stress. The present airfoil characteristics have been designed such that vibratory modes, which may result in high vibratory stresses at a resonant condition, are avoided. Accordingly, the modes do not occur in the normal engine operating speed range (near idle (line  440 )) and between minimum engine cruise (line  442 ) and redline (line  444 ). Vibratory modes, which are not predicted to have a high resonance response, are allowed to have a resonance condition in the normal operating range. As indicated, these evaluations may account for some or more of flowpath temperature and pressure, airfoil length, speed, etc. As a result, the evaluation and the subsequent iterative redesign of the airfoil is an airfoil which is unique for a specific engine in a specific operating condition. 
     During the design, the airfoil must be tuned such that the resonance points do not occur in the operating speed range of the engine for critical modes. To tune the airfoil, the resonance frequency must be changed, for example, by varying the airfoil length thickness, moment of inertia, or other parameters. These parameters are modified until the graphical intersections representing unwanted resonance occur outside the operating speed range, or at least outside key operating conditions within the operating speed range. This should be done for each the first four (or more) vibratory modes of the airfoil (1EB, 1T, 1CWB, 1SWB), and the airfoil should be tuned for varying excitation sources. 
     In  FIG. 10 , the idle speed is shown as  440 , the minimum cruise speed is shown as  442 , and the redline speed is shown as  444 . Idle speed is important because the engine spends much time at idle. Tuning out resonance at min cruise and redline speeds are important because engines typically cannot avoid these speeds. A resonance at an excitation frequency at an intermediate speed may be avoided by slightly increasing or decreasing speed. 
     As an example from  FIG. 10 , it is seen that there are two resonance conditions. That is, the 1st stiff-wise bending resonance mode (line  422 ) crosses two excitation lines, which are lines  406  and  408 . These two resonance conditions occur between the engine idle speed (line  440 ) and the engine minimum cruise speed (line  442 ). It should be understood that regardless of the particular mode, it is desirable to design an airfoil that at least avoids resonance at speed lines  440  and  442 . Resonance between lines  440  and  442  is an acceptable location for a resonance to occur and is unique for this airfoil in this engine. 
     The disclosed airfoil is subject to damage from wear and foreign object debris (FOD) during engine operation. Pieces of the airfoil may be broken off, for example, from the tip, leading edge and/or trailing edge resulting in an altered or unrestored mode resonance frequency for the airfoil, which deviates from at least one of the desired mode resonance frequencies indicated in the Table(s). One or more repair procedures are employed (e.g., welding a piece onto the airfoil and/or machining a grafted piece) to repair the airfoil and restore the geometry and integrity of the airfoil. The repair procedure restores the unrestored mode resonance frequency to again correspond to the desired mode resonance frequencies indicated in the Table(s). 
     It should also be understood that although a particular component arrangement is disclosed in the illustrated embodiment, other arrangements will benefit herefrom. Although particular step sequences are shown, described, and claimed, it should be understood that steps may be performed in any order, separated or combined unless otherwise indicated and will still benefit from the present invention. 
     Although the different examples have specific components shown in the illustrations, embodiments of this invention are not limited to those particular combinations. It is possible to use some of the components or features from one of the examples in combination with features or components from another one of the examples. 
     Although an example embodiment has been disclosed, a worker of ordinary skill in this art would recognize that certain modifications would come within the scope of the claims. For that reason, the following claims should be studied to determine their true scope and content.