Abstract:
A method and apparatus for ordering blades in a rotatable machine is provided. The machine includes a plurality of blades that extend radially outwardly from a rotor. The method includes determining a moment weight of each blade in a row of blades, determining a geometric parameter of each blade in the same row of blades, and determining a mapping order of each blade using the moment weight and the geometric parameter. The apparatus includes a computer system that includes a software product code segment for minimizing imbalance in a bladed rotor wherein the segment is configured to receive a moment weight value for each blade to be installed in said rotor, receive a geometric parameter value for each blade to be installed in said rotor, calculate a blade location on the rotor based on the received values, and generate a blade map based on the calculated location.

Description:
BACKGROUND OF THE INVENTION  
       [0001]     This invention relates generally to gas turbine-engines and, more particularly, to methods and apparatus for ordering blades in rotatable machines.  
         [0002]     Gas turbines are used in different operating environments, such as, to provide propulsion for aircraft and/or to produce power in both land-based and sea-borne power systems. At least some known gas turbine engines include a core engine having, in serial flow arrangement, a fan assembly and a high pressure compressor that compress airflow entering the engine. A combustor ignites a fuel-air mixture that is then channeled through a turbine nozzle assembly towards high and low pressure turbines. The turbines each include a plurality of rotor blades that extract rotational energy from airflow exiting the combustor.  
         [0003]     At least some known turbofan gas turbine engines include a fan assembly that includes a plurality of fan blades extending radially outwardly therefrom. During normal operation, gas turbine engines may experience high rotational speeds, and any imbalance of the rotor may induce vibrational stresses to the rotor and/or rotor bearings and/or support structures. Over time, continued operation with such stresses may lead to premature failure of the bearings, bearing support structure, and/or rotor components.  
         [0004]     Moreover, at least some known commercial jet engine fans operate with a relative blade tip Mach number in the transonic regime and may be subject to an operating characteristic called multiple-pure-tone (MPT) noise, or buzzsaw noise. Such noise may occur if at least some blades are oriented differently relative to other blades extending around the circumference of the fan case. Moreover, such noise may occur if blade-to-blade geometry variations exist within the fan. As a result, variations may exist within the fan assembly in the amplitude (strength) and/or spacing of the shockwaves originating from those portions of the blades that have sonic or supersonic velocities. Specifically, at axial locations close to the fan blades, the noise due to the shock waves is generally at multiples of the fan shaft per revolution frequency, which is the frequency with which one point on the shaft passes any particular fixed point as it rotates.  
         [0005]     Shock waves of different strengths may propagate at different speeds. Accordingly, as the shock waves travel away from the blades, the noise at a blade passing frequency degenerates into a broad spectrum of lower frequency tones as the shock waves merge with each other. Buzzsaw noise may be an issue with passenger annoyance and comfort, and may also adversely affect community noise levels.  
         [0006]     To facilitate minimizing imbalance and multiple pure tone noise of the fan during operation, at least some known fan assemblies are assembled in a controlled manner. For example, one control that may be used in assembling fan rotors involves mapping each fan blade into specific slots in the fan base. Within other known fan assemblies, a moment weight of each fan blade is determined and is used to map each blade into specific fan base slots. However, because the geometry of adjacent blades may be different, during operation a rotor may still experience a shift in balance and/or pure tone noise that is not associated with the moment weight of each blade but due to different aerodynamic loading between blades.  
       BRIEF DESCRIPTION OF THE INVENTION  
       [0007]     In one embodiment, a computer-implemented method of ordering blades in a rotatable machine is provided. The rotatable machine may include a plurality of blades that extend radially outwardly from a rotor. The method includes receiving a geometric parameter measurement of each blade in a row of blades, determining a root sum squared value of a difference of the geometric parameter measurement between adjacent blades in the row of blades, and determining a sequence map of each blade using root sum squared value of the difference of the geometric parameter measurement between adjacent blades in the row of blades.  
         [0008]     In another embodiment, a rotor assembly is provided. The rotor assembly includes a disk having a plurality of circumferentially-spaced blade root slots defined therein, and a plurality of blades, each blade having a root, a tip, and an airfoil therebetween, each blade is positioned within a pre-determined slot based on a blade map wherein the blade map is generated by a computer system that is configured to receive a geometric parameter measurement of each blade in a row of blades, determine a root sum squared value of a difference of the geometric parameter measurement between adjacent blades in the row of blades, and determine a sequence map of each blade using root sum squared value of the difference of the geometric parameter measurement between adjacent blades in the row of blades.  
         [0009]     In yet another embodiment, a computer system including a software product code segment for facilitating reducing multiple pure tone noise and imbalance in a bladed rotor is provided. The software code segment is programmed to receive a geometric parameter measurement of each blade in a row of blades, determine a root sum squared value of a difference of the geometric parameter measurement between adjacent blades in the row of blades, and determine a sequence map of each blade using root sum squared value of the difference of the geometric parameter measurement between adjacent blades in the row of blades. 
     
    
     BRIEF DESCRIPTION OF THE DRAWINGS  
       [0010]      FIG. 1  is a schematic illustration of an exemplary gas turbine engine;  
         [0011]      FIG. 2  is an exploded perspective view of an exemplary fan rotor and blading assembly that may be used with the gas turbine engine shown in  FIG. 1 ;  
         [0012]      FIG. 3  is a cross-sectional view of an exemplary fan blade taken along line  3 - 3  shown in  FIG. 1 ;  
         [0013]      FIG. 4  is a flow diagram of an exemplary method for ordering blades in a rotatable machine, such as the turbine engine shown in  FIG. 1 ; and  
         [0014]      FIG. 5  is a simplified block diagram of an exemplary blade mapping computer system. 
     
    
     DETAILED DESCRIPTION OF THE INVENTION  
       [0015]      FIG. 1  is a schematic illustration of an exemplary gas turbine engine  10  including a rotor  11  that includes a low-pressure compressor  12 , a high-pressure compressor  14 , and a combustor  16 . Engine  10  also includes a high-pressure turbine  18 , a low-pressure turbine  20 , an exhaust frame  22  and a casing  24 . A first shaft  26  couples low-pressure compressor  12  and low-pressure turbine  20 , and a second shaft  28  couples high-pressure compressor  14  and high-pressure turbine  18 . Engine  10  has an axis of symmetry  32  extending from an upstream side  34  of engine  10  aft to a downstream side  36  of engine  10 . Rotor  11  also includes a fan  38 , which includes at least one row of airfoil-shaped fan blades  40  attached to a hub member or disk  42 . Blades  40  are substantially identical with respect to each other blade  40 , except that there are some small differences due to manufacturing tolerances. Blades  40  are coupled to disk  42  in a substantially equi-angularly spaced relationship to each other. In one embodiment, gas turbine engine  10  is a GE90 engine commercially available from General Electric Company, Cincinnati, Ohio.  
         [0016]     In operation, air flows through low-pressure compressor  12  and compressed air is supplied to high-pressure compressor  14 . Highly compressed air is delivered to combustor  16 . Combustion gases  44  from combustor  16  propel turbines  18  and  20 . High pressure turbine  18  rotates second shaft  28  and high pressure compressor  14 , while low pressure turbine  20  rotates first shaft  26  and low pressure compressor  12  about axis  32 . During some engine operations, such as during takeoff operations and other operating periods when engine power output is relatively high, fan  38  rotates such that a radially outer portion of blades  40  attains supersonic velocity. As a result, the supersonically rotating portions of blades  40  may produce shockwaves, which can be heard as noise. The noise may be spread over a broad tonal range, from many multiples of blade passing frequency down to the disk rotational frequency.  
         [0017]      FIG. 2  is an exploded perspective view of an exemplary composite blade  100  and fan rotor disk  102  that may be used with gas turbine engine  10 . A plurality of circumferentially-spaced blades  100  are supported by rotor disk or drum  102  through a dovetail slot  104 . Each blade  100  includes an airfoil  106  that extends between a dovetail root  108  and a blade tip  110  such that each blade  100  is supported through dovetail root  108  and dovetail slot  104  by rotor  102 . Blade  100  is representative of the plurality of circumferentially-spaced blades  100  that are each mapped into a specific slot  104  based on measured parameters of blade  100 . In the exemplary embodiment, each blade  100  includes a composite airfoil  106  that includes a plurality of layered composite plies (not shown). More specifically, each blade  100  includes a first plurality of structural and load carrying airfoil plies in airfoil  106  and a second plurality of root plies in root  108 .  
         [0018]      FIG. 3  is a cross-sectional view of an exemplary fan blade  40  taken along line  3 - 3  (shown in  FIG. 1 ). An angle  150  represents an amount of section stagger angle of blade  40  at the cross-section of blade  40  illustrated. Generally, angle  150  is dependent on a radial distance from axis  32  to the cross-section of interest. In the exemplary embodiment, angle  150  is measured between a chord  152  at the cross-section and fan axis  32  of symmetry. A thickness  154  of blade  40  represents the thickness of a leading edge  156  of blade  40 . Leading edge  156  is in relation to airflow  158  through fan  38 . Each blade  40  includes a radial axis  160 .  
         [0019]     Factors of blade design that may affect pure multiple tone noise may be, for example, but are not limited to, differences of angle  150  from blade-to-blade, differences of thickness  154  from blade-to-blade, differences in the curvature of the blade airfoil at respective sections from blade-to-blade, and variations of spacing between adjacent blades.  
         [0020]      FIG. 4  is a flow diagram of an exemplary method  300  that may be used for ordering blades in a rotatable machine, such as turbine  10  (shown in  FIG. 1 ). In the exemplary embodiment, the machine is a gas turbine engine that includes a rotor, such as rotor  11 , (shown in  FIG. 1 ), that is rotatable about a longitudinal axis of symmetry of the engine. The rotor includes circumferentially-spaced slots for receiving the blades such that the blades extend radially between a blade root and a blade tip from the slots.  
         [0021]     Method  300  includes receiving  302  a geometric parameter measurement of each blade in a row of blades. The fan blade geometric parameter may be based on a determination by an acoustics specialist and fan aerodynamics specialists relative to a customer specification. The geometric parameter may be any of a plurality of measurable blade parameters that contribute to a difference of a ratio of blade inlet area to blade exit area for adjacent blades. Such parameters may include, for example, but are not limited to, a blade section stagger angle, a blade tangential shift, and a blade thickness.  
         [0022]     Each adjacent pair of blades defines a volume between the blades. The volume includes an inlet area extending between adjacent leading edges of the blades and an exit area extending between adjacent trailing edges of the blades. An inlet area to exit area ratio may be used to determine the geometric parameter that is used to map the blades into the rotor.  
         [0023]     The blade section stagger angle may be defined as a rotation of at least a portion of a blade about a radial axis through a central region of the blade. The axis of stagger angle may be offset from a center radial axis of the blade, or may be coincident with the center radial axis. The blade tangential shift may be defined as a displacement of a blade tip in a circumferential direction in a plane of rotation of the row of blades containing the blade. The blade tangential shift may be used to quantify an amount that a blade is offset from a radial orientation and may also describe a blade that is bowed in the plane of rotation of the row of blades containing the blade. Blade thickness may refer to the thickness of the blade leading edge at a predetermined radial distance from the blade tip, the thickness of the blade trailing edge at a predetermined radial distance from the blade tip, and/or the thickness of the blade at a predetermined intermediate point at a predetermined radial distance from the blade tip. The geometric parameter measurement may be received from a blade manufacturer or may be determined after the blade is received at a manufacturing facility.  
         [0024]     Prior to positioning blades onto the rotor disk, an initial or starting blade map is determined  304 . A blade map may indicate a specific slot for each blade that will be assembled into the rotor and may indicate an order of installation of the blades. The starting position may be a “virtual” position, in that the blades are simulated being installed using a computer model of the rotor and blades. Subsequent iterative maps of blade location may also be virtual maps until a predetermined endpoint is reached during iteration, when a final blade map may be displayed and/or printed.  
         [0025]     A root sum squared value of a difference of the selected geometric parameter measurement between adjacent blades in the row of blades may be determined  306  from blade geometry data supplied by the blade manufacturer or may be determined by the manufacturing facility after receipt. The following expression may be used to determine the root sum squared value: 
 
√{square root over (Σ(θ i+1 −θ i ) 2 )} where 
 
 θ i  and θ i+1  represent the selected geometric parameter selected for adjacent blades in a blade pair. 
 
         [0026]     For example, a blade section stagger angle difference between adjacent blades may be determined by calculating a ratio of the inlet area to exit area for each pair of blades installed in a starting position around the circumference of the rotor. To determine a mapping order, a computer including a processor and a program code segment configured to select and deselect blades may be utilized. Specifically, when blades are selected in complementary pairs, a first blade may be selected for positioning in a specific slot based on the root sum squared value of the difference of the selected geometric parameter between each pair of blades, a moment weight, and/or aerodynamic or geometric parameters. Blades are iteratively arranged in an order that facilitates minimizing a combination of the vector sum of the moment weight of all the blades to be positioned on the rotor disk and the root sum squared value of the difference of the selected geometric parameter between each pair of blades. During the process of minimizing this combination of parameters, it may be necessary to completely reorder the selected blades. The computer system may then display the resultant blade map and generate a report detailing the selection process. Additionally, manual entry of blade parameters and recalculation of the blade map are supported.  
         [0027]     The inlet area and/or exit area may be determined using a distance between adjacent blades at the same radial distance from the blade tip. Because at least some of the parameters that may be used to determine inlet area and exit area may be fixed, only a line distance may be used to determine ratio of the inlet area and outlet area. A moment weight of each blade in a row of blades may be determined  310  and a moment weight vector sum of the rotor may also be determined  312 . The moment weight may be determined by horizontally supporting a blade by its root in a device designed to measure moment weight. A moment weight is based not only on a pan weight of the blade, but also is based on a distribution of the weight of the blade along a radial distance extending between the blade root to the blade tip. In a rotating machine, an uneven distribution of moment weight of each blade spaced about the rotor may affect a balance condition of the rotor.  
         [0028]     Threshold values for the selected geometric parameters are determined  314 . The threshold values may be determined from an engineering or design requirement contained within a drawing or other technical or administrative document. The initial blade sequence is iteratively remapped  316  to reduce the root summed squared value of the difference of the geometric parameter between each adjacent blade, and reduce the moment weight vector sum of the rotor to values that are less than the respective predetermined values. When the root summed squared value of the difference of the geometric parameters between adjacent blades, and the moment weight vector sum of the rotor are reduced  318  to values that are less than the respective predetermined values, the final blade sequence map may be displayed  320  and/or output.  
         [0029]      FIG. 5  is a simplified block diagram of a blade mapping computer system  400 . As used herein, the term “computer” may include any processor-based or microprocessor-based system including systems using microcontrollers, reduced instruction set circuits (RISC), application specific integrated circuits (ASICs), logic circuits, and any other circuit or processor capable of executing the functions described herein. The above examples are exemplary only, and are thus not intended to limit in any way the definition and/or meaning of the term “computer”. Computer system  400  includes a server system  412  including a disk storage unit  413  for data storage, and a plurality of client sub-systems, also referred to as client systems  414 , connected to server system  412 . In one embodiment, client systems  414  are computers including a web browser, such that server system  412  is accessible to client systems  414  via the Internet. Client systems  414  are interconnected to the Internet through many interfaces including a network, such as a local area network (LAN) or a wide area network (WAN), dial-in-connections, cable modems and special high-speed ISDN lines. Client systems  414  could be any device capable of interconnecting to the Internet including a web-based phone, personal digital assistant (PDA), or other web-based connectable equipment. A database server  416  is connected to a database  418  containing information regarding engine components. In one embodiment, centralized database  418  is stored on server system  412  and can be accessed by potential users at one of client systems  414  by logging onto server system  412  through one of client systems  414 . In an alternative embodiment database  418  is stored remotely from server system  412  and may be non-centralized.  
         [0030]     Example embodiments of systems and methods that facilitate reducing multiple pure tone noise in aircraft gas turbine engine fans are described above in detail. A technical effect of the systems and methods described herein includes reducing overall circumferential pressure differences between adjacent blade pairs to minimize fan tonal noise, and therefore reducing aircraft passenger annoyance and community noise levels.  
         [0031]     The above-described blade mapping system is a cost-effective and highly reliable method and system that may be used for determining a blade map that reduces a root sum squared value of a difference of a geometric parameter measurement between adjacent blades to a value that is less than a predetermined threshold. The method also iteratively remaps the blades to reduce a rotor moment weight vector sum to a value that is less than a predetermined threshold. Each system is configured to receive a geometric parameter measurement and a moment weight value for each blade, determine an initial blade location on the rotor, and generate a blade map based on iteratively reducing the root sum squared value of a difference of the geometric parameter measurement value between adjacent blades and the rotor moment weight vector sum to values that are less than predetermined respective threshold values. Accordingly, the blade mapping method and system facilitates assembly, operation, and maintenance of machines, and in particular gas turbine engines, in a cost-effective and reliable manner.  
         [0032]     Exemplary embodiments of blade mapping method and system components are described above in detail. The components are not limited to the specific embodiments described herein, but rather, components of each system may be utilized independently and separately from other components described herein. Each blade mapping system component can also be used in combination with other blade mapping system components.  
         [0033]     While the invention has been described in terms of various specific embodiments, those skilled in the art will recognize that the invention can be practiced with modification within the spirit and scope of the claims.