System And Method For Monitoring Health Of Airfoils
Abstract:
A method is presented. The method includes the steps of determining normalized delta times of arrival corresponding to a plurality of blades based upon actual times of arrival corresponding to the plurality of blades, and determining static deflections of the plurality of blades by removing effects of one or more common factors from the normalized delta times of arrival corresponding to the plurality of blades.
Fig. 2
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Notices, Deadlines & Correspondence
SYSTEM AND METHOD FOR MONITORING HEALTH OF AIRFOILS
BACKGROUND
[0001] Embodiments of the disclosure relates generally to systems and methods for monitoring health of rotor blades or airfoils.
[0002] Rotor blades or airfoils play a crucial role in many devices with several examples including axial compressors, turbines, engines, turbo-machines, or the like. For example, an axial compressor has a series of stages with each stage comprising a row of rotor blades or airfoils followed by a row of static blades or static airfoils. Accordingly, each stage comprises a pair of rotor blades or airfoils and static airfoils. Typically, the rotor blades or airfoils increase the kinetic energy of a fluid that enters the axial compressor through an inlet. Furthermore, the static blades or static airfoils generally convert the increased kinetic energy of the fluid into static pressure through diffusion. Accordingly, the rotor blades or airfoils and static airfoils increase the pressure of the fluid.
[0003] Furthermore, the axial compressors that include the rotor blades or airfoils and the static airfoils have wide and varied applications. Axial compressors, for example, may be used in a number of devices, such as, land based gas turbines, jet engines, high speed ship engines, small scale power stations, or the like. In addition, the axial compressors may have other applications, such as, large volume air separation plants, blast furnace air, fluid catalytic cracking air, propane dehydrogenation, or the like.
[0004] The airfoils operate for long hours under extreme and varied operating conditions such as, high speed, pressure and temperature that affect the health of the airfoils. In addition to the extreme and varied operating conditions, certain other factors lead to fatigue and stress of the airfoils. The factors, for example, may include inertial forces including centrifugal force, pressure, resonant frequencies of the airfoils, vibrations in the airfoils, vibratory stresses, temperature stresses, reseating of the airfoils, load of the gas or other fluid, or the like. A prolonged increase in stress and fatigue over a period of time leads to defects and cracks in the airfoils. One or more of the cracks may widen with time to result in liberation of an airfoil or a portion of the airfoil. The liberation of airfoil may be hazardous for the device that includes the airfoils, and thus may lead to enormous monetary losses. In addition, it may be unsafe for people located near the device.
[0005] Accordingly, it is highly desirable to develop a system and method that may predict health of airfoils in real time. More particularly, it is desirable to develop a system and method that may detect and predict cracks or fractures in real time.
BRIEF DESCRIPTION
[0006] Briefly in accordance with one aspect of the technique, a method is presented. The method includes the steps of determining normalized delta times of arrival corresponding to a plurality of blades based upon actual times of arrival corresponding to the plurality of blades, and determining static deflections of the plurality of blades by removing effects of one or more common factors from the normalized delta times of arrival corresponding to the plurality of blades.
[0007] In accordance with an aspect, a system including a processing subsystem is presented. The processing subsystem determines normalized delta times of arrival corresponding to a plurality of blades based upon actual times of arrival corresponding to the plurality of blades, and generates static deflections of the plurality of blades by removing effects of one or more common factors from the normalized delta times of arrival corresponding to the plurality of blades.
[0008] In accordance with another aspect of the present systems a processing subsystem is presented. The processing subsystem determines a plurality of modes corresponding to a plurality of blades based upon normalized delta times of arrival corresponding to the plurality blades, determines a plurality of blade coefficients corresponding to the plurality of modes and the plurality of blades based upon the normalized delta times of arrival, identifies one or more blade coefficients in the plurality of blade coefficients that correspond to common modes in the plurality of modes, equating the one or more blade coefficients in the plurality of blade coefficients to zero to generate a reconstruction matrix, and determines static deflections corresponding to the blades based upon the normalized delta times of arrival and the plurality of modes.
DRAWINGS
[0009] These and other features, aspects, and advantages of the present invention will become better understood when the following detailed description is read with reference to the accompanying drawings in which like characters represent like parts throughout the drawings, wherein:
[0010] FIG. 1 is an exemplary diagrammatic illustration of a blade health monitoring system, in accordance with an embodiment of the present system;
[0011] FIG. 2 is a flow chart representing an exemplary method for determining static deflection, in accordance with an embodiment of the present techniques;
[0012] Fig. 3 is a flowchart representing an exemplary method for determining the normalized delta TOAs referred to in Fig. 2, in accordance with an embodiment of the present techniques;
[0013] Fig. 4 is an exemplary graphical representation of actual TOAs that are computed using a robust least squares technique, in accordance with one embodiment of the present techniques;
[0014] Fig. 5 is a flowchart representing an exemplary method for determining the plurality of modes and a plurality of blade coefficients referred to in Fig. 2, in accordance with an embodiment of the present techniques;
[0015] Fig.6 is a flowchart representing an exemplary method for determining common modes referred to in Fig. 2, in accordance with an embodiment of the present techniques;
[0016] Fig. 7(a) and Fig. 7(b) are exemplary graphical representations of coefficients corresponding to two modes for identification of coefficients corresponding to common modes, in accordance with an embodiment of the techniques;
[0017] Fig. 8 is a graphical representation of signals representative of normalized delta TOAs, common modes or blade coefficients corresponding to common modes, and static deflection corresponding to a plurality of blades are shown to explain determination of static deflection, in accordance with one embodiment of the present techniques; and
[0018] Fig. 9 is a graphical representation of signals representative of static deflections of blades that are shown to explain monitoring of the health of the blades.
DETAILED DESCRIPTION
[0019] As discussed in detail below, embodiments of the present systems and techniques evaluate the health of one or more blades or airfoils. More particularly, the present systems and techniques determine static deflection of the blades or airfoils. The static deflection of the blades, for example, may be used to monitor the health of the blades. Hereinafter, the terms "airfoils" and "blades" will be used interchangeably. The static deflection, for example, may be used to refer to a steady change in an original or expected position of a blade from the expected or original position of the blade.
[0020] In operation during rotations of blades, times of arrival (TOAs) (hereinafter referred to as actual TOAs) of the blades at a reference position may vary from expected TOAs due to one or more cracks or defects in the blades. Accordingly, the variation in the TOAs of the blades may be used to determine the static deflection of the blades. As used herein, the term "expected TO A" may be used to refer to a TOA of a blade at a reference position when there are no defects or cracks in the blade and the blade is working in an ideal situation, load conditions are optimal, and the vibrations in the blade are minimal.
[0021] In addition to the cracks or defects in the blades, the actual TOAs may also vary due to effects of one or more common factors. As used herein, the term "common factors" is used to refer to reasons that are common to blades in a device, wherein the reasons impact (for example: advances or delays) actual TOAs corresponding to the blades. The common factors, for example, may include operational parameters, reseating of blades, and the like. The operational parameters, for example, may include an inlet guide vane (IGV) angle, a load variation, reseating of a blade, variation of speed, temperature, speed, or the like.
[0022] As used herein, the term "reseating of a blade" may be used to refer to a locking of a blade at a position different from the original or expected position of the blade in joints, such as, a dovetail joint. Typically, the blades are fastened to a rotor via one or more joints, such as, dovetail joints. During start-up of a device that includes the blades, the blades may shift from their original positions in the joints and may lock in the joints at positions that are different from the original positions of the blades. By way of an example, the device may include a gas turbine, a compressor, or the like. The locking of the blades in the joints at the positions different from the original positions of the blades is referred to as reseating of the blades. The change in the positions of the blades may vary actual TO As of the blades.
[0023] Consequently, due to the effects of the common factors and the cracks or defects in the blades on actual TO As corresponding to the blades, the static deflections of the blades vary from an exact or accurate static deflection. Accordingly, to monitor the health of the blades or determine cracks or defects in the blades, it is desirable to negate the effects of the common factors on actual TOAs corresponding to the blades. Certain embodiments of the present systems and techniques remove the effects of the common factors to determine static deflection of blades.
[0024] FIG. 1 is a diagrammatic illustration of a blade health monitoring system 10, in accordance with an embodiment of the present system. As shown in FIG. 1, the system 10 includes one or more blades or airfoils 12 that are monitored by the system 10 to determine static deflection of the blades 12. Furthermore, the system 10 determines the health of the blades 12 based upon the static deflection of the blades 12. As shown in the presently contemplated configuration, the system 10 includes one or more sensors 14, 16. Each of the sensors 14, 16 generate blade passing signals (BPS) 18, 20, respectively that are representative of actual times of arrival (TOAs) of the blades 12 at a reference point. In one embodiment, the sensors 14, 16 sense an arrival of the one or more blades 12 at the reference point to generate the BPS 18, 20. The reference point, for example, may be underneath the sensors 14, 16 or adjacent to the sensors 14, 16. In an embodiment, each of the BPS 18, 20 are sampled and/or measured for a particular time period and is used for determining actual TOAs of a blade. The actual TOAs, for example, may be measured in units of time or degrees.
[0025] In one embodiment, the sensors 14, 16 may sense an arrival of the leading edge of the one or more blades 12 to generate the BPS 18, 20. In another embodiment, the sensors 14, 16 may sense an arrival of the trailing edge of the one or more blades 12 to generate the BPS 18, 20. In still another embodiment, the sensor 14 may sense an arrival of the leading edge of the one or more blades 12 to generate the BPS 18, and the sensor 16 may sense an arrival of the trailing edge of the one or more blades 12 to generate the BPS 20, or vice versa. The sensors 14,16, for example, may be mounted adjacent to the one or more blades 12 on a stationary object in a position such that an arrival of the one or more blades 12 may be sensed efficiently. In one embodiment, at least one of the sensors 14, 16 is mounted on a casing (not shown) of the one or more blades 12. By way of a non-limiting example, the sensors 14, 16 may be magnetic sensors, capacitive sensors, eddy current sensors, or the like.
[0026] As illustrated in the presently contemplated configuration, the BPS 18, 20 are received by a processing subsystem 22. The processing subsystem 22 determines actual TOAs of the one or more blades 12 based upon the BPS 18, 20. Furthermore, the processing subsystem 22 determines static deflection of the one or more blades 12 based upon the actual TOAs of the one or more blades 12. More particularly, the processing subsystem 22 is configured to determine the static deflection of the one or more of the blades 12 by processing the actual TOAs of the one or more blades 12. The actual TOAs of the blades 12 may be affected due to one or more common factors. As used herein, the term "common factors" is used to refer to reasons that are common to all blades in a device, wherein the reasons impact (for example: advances or delays) the actual TOAs corresponding to the blades. The common factors, for example, may include operational parameters, reseating of blades, and the like.
[0027] If static deflections of the blades 12 are determined based upon such actual TOAs without removing the effects of the common factors, then such static deflections may wrongly suggest cracks in the one or more of the blades 12, even though there is no crack or defect in the blades 12. Therefore, in the presently contemplated techniques, the processing subsystem 22, for example, determines static deflections of the blades 12 by removing the effects of the common factors from the actual TOAs corresponding to the blades 12. In one embodiment, the processing subsystem 22, for example, may determine static deflection corresponding to the blades 12 by removing the effects of the common factors from normalized delta TOAs that are determined based upon the actual TOAs corresponding to the blades 12. The effects of the common factors, for example, may be removed by applying techniques comprising a principal components analysis technique, a singular value decomposition technique, an independent component analysis technique, or combinations thereof. As used herein, the term "normalized delta TOA" refers to a numerical value corresponding to an actual TOA of a blade in a plurality of blades, wherein the numerical value is determined based upon actual TOAs corresponding to the plurality of blades, and a blade spacing parameter. The determination of the normalized delta TOAs and the blade spacing parameter will be explained in detail with reference to Fig. 2 and Fig. 3.
[0028] In one embodiment, the processing subsystem 22 determines the static deflection corresponding to the blades 12 by applying a principal component analysis technique (PCA) to the actual TOAs or normalized delta TOAs. Accordingly, the processing subsystem 22 may remove the effects of common factors from the actual TOAs by applying a principal components analysis technique to the actual TOAs. In one embodiment, the processing subsystem removes the effects of the common factors from the actual TOAs using techniques including a principal components analysis technique, a singular value decomposition technique, an independent component analysis technique, or combinations thereof. The determination of the static deflection shall be explained in greater detail with reference to Fig. 2 to Fig. 6. In one embodiment, the processing subsystem 22 may have a data repository 24 that stores data, such as, static deflection, dynamic deflection, TOA, delta TOA, any intermediate data, or the like.
[0029] It is noted that in the presently contemplated configuration, the effects of the common factors, such as, operational parameters are removed from the actual TOAs without recourse to any data relating to the common factors, such as, the operational parameters, reseating of blades, , and the like. Accordingly it is noted that in the presently contemplated techniques, data from external devices, such as, an onsite monitoring device or any other device is not required for removal of effects of common factors from the actual TOAs, or the normalized delta TOAs. The operational parameters, for example, may include an inlet guide vane (IGV) angle, a load variation, reseating of a blade, variation of speed, temperature, speed, or the like.
[0030] Referring now to FIG. 2, a flowchart representing an exemplary method 200 for determining static deflection of a plurality of blades, in accordance with an embodiment of the present techniques, is depicted. The plurality of blades, for example, may be the blades 12 (see FIG. 1). Hereinafter, for ease of understanding, the determination of the static deflection shall be explained with reference to the blades 12. At step 202, blade passing signals (BPS) corresponding to the blades 12 may be received by a processing subsystem, such as, the processing subsystem 22 (see FIG. 1). As previously noted with reference to Fig. 1, the BPS may be generated by a sensor, such as, the sensors 14, 16 (see Fig. 1). The BPS, for example, may be the BPS 18, 20. (See Fig. 1).
[0031] Furthermore, at step 204 actual times of arrival (TOAs) 206 of the blades 12 are determined by the processing subsystem. The processing subsystem determines the actual TOAs by sampling the BPS. Particularly, the processing subsystem determines one or more actual TOAs corresponding to a blade utilizing a BPS corresponding to the blade. At step 208, normalized delta TOAs 210 corresponding to the blades 12 may be determined. As used herein, the term "normalized delta TO A" refers to a numerical value corresponding to an actual TOA of a blade in a plurality of blades, wherein the numerical value is determined based upon actual TOAs corresponding to the plurality of blades and a blade spacing parameter. The normalized delta TOAs 210, for example may be determined by the processing subsystem. In one embodiment, the normalized delta TOAs 210 is determined by applying a robust least squares technique or a weighted least squares technique on the actual TOAs 206. The determination of the normalized delta TOAs 210 using the robust least squares technique eliminates the explicit normalization steps. The determination of the normalized delta TOAs using the robust least squares technique reduces the extreme sensitivity to one or more outlier actual TOA's, when the one or more outlier actual TOA's exist; for example, actual TOA's of a cracked blade. In one embodiment, the determination of the normalized delta TOAs 210 using the robust least squares techniques generates the normalized delta TOAs that has been normalized for effects of load without recourse to load data. The determination of normalized delta TOAs is explained in greater detail with reference to Fig. 3 and Fig. 4. At step 212, a modes matrix M or a plurality of modes 214 may be determined. Furthermore, at step 212, a coefficients matrix U or a plurality of blade coefficients 215 corresponding to the plurality of modes 214 may be determined. The modes matrix M 214 and the coefficients matrix U 215, for example are determined by applying a principal component analysis technique on the normalized delta TO As 210. It is noted that while the presently contemplated technique explains one embodiment for determination of the static deflections and/or the modes matrix using the principal components analysis technique, other techniques, such as, a singular value decomposition technique, an independent components analysis technique, or combinations thereof may be used. Particularly, the modes matrix M 214, for example, may be determined based upon the normalized delta TOAs 210, and an Eigenvector matrix V determined based upon the normalized delta TOAs 210. The determination of the Eigenvector matrix V is explained in greater detail with reference to Fig. 5. The modes matrix M 214 represents a plurality of modes 214 corresponding to the blades 12.
In one embodiment, each row in the modes matrix M 214 represents a mode in the plurality of modes 214. In another embodiment, each column in the modes matrix M 214 represents a mode in the plurality of modes 214. In one embodiment, the plurality of modes 214 or the modes matrix M may be determined by using the following equation: M=X*V (1) where M is a modes matrix, X is a matrix of normalized delta TOAs, and V is an Eigenvector matrix.
[0034] Furthermore, at step 212, the plurality of blade coefficients or the coefficients matrix U 215 may be determined. The coefficients matrix U 215, for example, may be determined based upon the Eigenvector matrix V. The coefficients matrix U 215 represents blade coefficients of the blades 12 corresponding to the plurality of modes 214. In one embodiment when rows in the modes matrix M 214 represent the plurality of modes 214, columns in the coefficients matrix U 215 represents blade coefficients of the blades 12 corresponding to the plurality of modes 214, or vice versa. For example, a row in the coefficients matrix U 215 may represent blade coefficients corresponding to a mode represented by a column in the modes matrix 215, or vice versa. For example, 1st row of the coefficients matrix U may represent blade coefficients of the blades 12 corresponding to a mode, wherein the mode is represented by a 1st column in the modes matrix M 214. Exemplary graphical representation of two rows of a coefficients matrix U is shown in Fig. 7(a) and Fig. 7(b), respectively.
[0035] Furthermore, at step 216, blade coefficients in the coefficients matrix U 215 that correspond to common modes in the plurality of modes 214 are determined. As used herein, the term "common mode" is used to refer to a mode corresponding to blade coefficients of a plurality of blades, wherein the blade coefficients fall within a range. In one embodiment, a range is determined based upon the blade coefficients of blades corresponding to a mode in real-time. In another embodiment, the range is determined based upon common mode selection thresholds. In another embodiment, the blade coefficients in the coefficients matrix U 215 that correspond to common modes, for example, are identified based upon respective common mode selection thresholds. Identification of the blade coefficients that correspond to common modes and determination of common mode selection thresholds is explained in greater detail with reference to Fig. 6, Fig. 7(a) and Fig. 7(b), in accordance with one embodiment of the present techniques.
[0036] Furthermore, at step 218, a reconstruction matrix Ui is generated by equating the blade coefficients corresponding to the common modes in the coefficients matrix U 215 equal to zero. Subsequently at step 220, static deflections 222 corresponding to the blades 12 are determined using the reconstruction matrix Ui and the modes matrix M. The static deflection, for example, may be determined using the following equation (2): wherein Y represents static deflections, M represents a modes matrix, and Ui represents a reconstruction matrix. Subsequently at step 224, the health of the blades 12 may be analyzed based upon the static deflections 222. In one embodiment, when one or more of the static deflections 222 corresponding to one or more of the blades 12 exceed a determined threshold, then faults, defects or cracks in the one or more of the blades 12 may be declared. It is noted that in one embodiment, the multiplication of the modes matrix M 214 to the reconstruction matrix Ui results in removal of effects of common modes in the static deflections 222. Particularly, the multiplication of the modes matrix M and the reconstruction matrix £/, results in the removal of the effects of the common factors from the normalized delta TO As 210 to determine the static deflections 22 of the blades 12.
[0037] Referring now to Fig. 3, a flowchart representing an exemplary method 300 for determining the normalized delta TOAs 210 corresponding to the blades 12, in accordance with an embodiment of the techniques, is depicted. In one embodiment, Fig. 3 explains step 208 in Fig. 2 in greater detail. As previously noted, reference numeral 206 is representative of actual times of arrival (TOAs) corresponding to the blades 12. At step 302, a line may be fitted on the actual TOAs 206 using a robust least squares technique. An exemplary fitting of a line on actual TOAs using a robust least squares technique is shown in Fig. 4.
[0038] At step 304, an inter-blade spacing parameter and a load parameter may be determined. The inter-blade spacing parameter and the load parameter may be determined using the line fitted on the actual TOAs 206. An exemplary determination of an inter-blade spacing parameter and a load parameter is described with reference to Fig. 4. At step 306, normalized delta TOAs 210 may be determined corresponding to one or more of the blades 12 based upon the inter-blade spacing parameter, the actual TOAs 206 and the load parameter. Particularly, a normalized delta TOA corresponding to a blade may be determined based upon a corresponding actual time of arrival (TOA), a corresponding inter-blade spacing parameter and the load parameter. In one embodiment, the normalized delta TOAs may be determined using the following equation (3):
NormAOj {k)=0A{k)-[X(k){j-\) +