TURBINE BLADE FATIGUE MONITOR

Abstract: An on-line vibratory fatigue monitor measures displacement of an object such as the blade of a turbine rotor to generate a displacement signal produced by proximity sensors and calculates accumulated fatigue in the object in dependence upon the displacement signal. The signals are digitized and processed, by taking a Hilbert transform, to detect the amplitude envelope and instantaneous frequency of the displacement. The amplitude and frequency are combined with steady state stress on the object to determine fatigue usage which is accumulated by constantly monitoring vibratory displace­ ment and changes in the steady state stress.

Description: BACKGROUND OF THE INVENTION Field of the Invention The present invention is generally related to measurement of fatigue caused by vibration and, more particularly, to the measurement of accumulated metal fatigue in the rotor of a turbine. Description of the Related Art Conventionally, stresses in turbine blades, like in other devices, are measured using strain gauges which attach directly to the turbine blade and communicate to monitoring equipment outside the turbine via slip rings or telemetry. An alternative system has undergone development at the Arnold Engineering Development Center of the U.S. Air Force Systems Command. The Arnold system utilizes line-focusing photo detectors which provide non-interference measurement of jet engine turbine rotor blade deflection. The sensors are closely spaced on the periphery of the engine casing with each sensor radially aligned and the group of sensors aligned with the path of the rotor blade tips. Two sensors are used for detecting non-integral vibration, i.e., vibration at frequencies other than multiples of the rotation speed. Four sensors are used for detecting integral vibration, i.e., vibration at a frequency which is a multiple of the rotation speed. The signals produced by these sensors can be processed with reference to a once-per-revolution signal to determine amplitude, frequency and phase of the vibration of the each blade in a row. An additional set of these sensors is required for each row which is monitored. Upon the deflection data provided by the sensors, stress information for all blades in each instrumented row can be determined on-line by using transfer functions to convert the deflection data to stress. These transfer functions can be determined using finite-element analysis and bench-testing of each row of blades before operational testing. While the information provided by the Arnold system is useful, particularly in testing recently serviced turbines, additional information is desirable for an on-line system which is used to monitor a turbine during operation. On-line blade monitoring is disclosed in the following patents: U.S. Patent No. 4,518,917 discloses an apparatus for continuously monitoring the vibration of the blades of turbine rotors so as to determine abnormal turbine operating conditions. British Patent No. 2,143,037 relates to the monitoring of vibration of the blades of turbine rotors wherein two spaced sensors determine blade distance which varies as a result of fibration and, thus, permit the monitoring of blade vibration during turbine operation. It is the object of the present invention to utilize on-line blade vibration monitoring equipment to accurately determine blade fatigue or expired expectancy that is rather remaining life of a turbine blade as a result of vibration and load stresses. With this object in view, the present invention resides in a continuous measuring apparatus for measurement of accumulated mechanical fatigue of vibrating members of a bladed turbine rotor so as to compute "fatigue usage" as a measure of accumulated fatigue to learn regarding a remaining life of the vibrating members before fatigue breakdown, said apparatus comprising a rotor torque sensor, sensors mounted proximate to a vibrating member for generating a displacement signal indicating displacement of said vibrating members caused by vibration of the member; and fatigue accumulation means for calculating "fatigue usage" in the member in dependence upon the displacement signal, characterized in that said fatigue accumulation means includes means subjecting the displacement signal generated by said sensors to a Hilbert transformation for determining frequency and amplitude of vibration of the turbine blades and means utilizing Goodman's law as applied to the frequency and amplitude of the vibration of the turbine blades with the addition of torque stress as determined by the rotor torque sensor to compute fatigue usage by accumulating fatigue of turbine blades. It also resides in an on-line fatigue measuring method for measuring fatigue of turbine blades in a turbine, having at least two vibration sensors positioned outside a row of the turbine blades for detecting passage of the turbine blades without contact therewith so as to produce sensor signals; and a torque sensor for sensing torque generating by the turbine characterized by the steps of: using Hilbert transformation for determining frequency and amplitude of vibration of the turbine blades from the sensor signals produced by said two sensors; and computing fatigue usage as an accumulation of fatigue of the turbine blades by application of Goodman's law to the frequency and the amplitude of the vibration of the turbine blades with the addition of steady stress on the turbine blades the steady stress being determined in dependence upon the torque sensed by the torque sensor. Preferably at least two sensors are positioned outside a path taken by the turbine blades. When N sensors are used, the vibration and fatigue usage to the n/2'th harmonic can be computed. Twenty-four sensors will give the effect of all harmonics to the 12th, but only fewer sensors are necessary if it can be determined that fewer harmonics are active. The invention will become more readily apparent from the following description of a preferred embodiment, given by way of example only, in the accompanying drawing wherein: Fig. 1 is a perspective view of a turbine shaft and one row of blades with sensors indicated as used in the context of the present invention; Fig. 2 is a block diagram of a preferred embodiment of the present invention; Fig. 3 is a schematic diagram illustrating how a blade is identified by the system; Figs. 4A and 4B are graphical illustrations of displacement of a turbine blade from an expected position caused by vibration; Fig. 5 is a flowchart of the method used by the present invention to assess accumulated fatigue; and Fig. 6 is a graphical representation of vibration of the turbine blade. Many types of devices are subject to stresses that build up or accumulate fatigue which eventually causes defects to appear in the material of which the device is made. The amount of fatigue which a device can withstand is termed "fatigue life" and the amount of fatigue which a device has withstood is termed "fatigue usage". By accumulating the fatigue usage, the remaining fatigue life can be calculated from equation (1). Equation (1) can be derived from Goodman's law and Miner's hypothesis, where ε a (t) is the actual vibratory stress, ε F is the stress which causes failure from application of a single load ignoring the formation of a plastic hinge, ε m (t) is a slowly varying or essentially steady stress, ε₁ is the limit stress which causes failure at, e.g., the millionth vibration, and F(t) is the frequency of the vibration. The values ε F and ε₁ are conventionally determined for a specific object by laboratory measurement or finite element analysis. In the case of a turbine rotor, within each row the blades are ordinarily shaped the same, but one row is different from another. Therefore, the values ε F and ε₁ would be determined separately for each row of turbine blades. Similarly, the steady stress ε m on an object to be monitored by the present invention must be determined beforehand as a function of measurable values. In the case of turbine blades, the torque generated by the turbine could be directly measured or calculated from measurements of inlet enthalpy H₁, outlet enthalpy H₂, angular speed ω and mass flow rate m ˙, which may then be combined with stage efficiency n, mean blade diameter r b and the number of blades per row M b to calculate a relationship between the steady stress ε m and the torque as indicated in equation (2). ε m ∼ m (H₁-H₂)n/ω M b r b (2) Thus, knowing the limit stress ε₁, single load failure stress ε F and the distribution of torque in a turbine, the fatigue usage can be calculated from torque, measured either directly or indirectly, and the amplitude and frequency of vibrations of individual turbine blades. The actual vibratory stress ε a (t) relationship to amplitude of blade tip deflection can be measured using a stress/strain gauge mounted on a disassembled turbine rotor. A conventional rotor shaft 10 of a turbine, together with some of the turbine blades 12 in one row 14 of turbine blades is illustrated in Fig. 1. In accordance with the present invention, sensors 16-22 are positioned outside a path taken by the turbine blades in radial alignment with the blades. Only seven sensors are fully illustrated in Fig. 1, but additional sensors could be positioned as indicated by the tick marks around the turbine blade disk 14. As illustrated in Fig. 2, several groups 23 of sensors are provided, one group 23 for each of the rows of the turbine whose blades are to be monitored. This may not be every row, depending upon the construction of the turbine, maintenance experience, etc. For example, if within several rows of blades, experience shows that the first breakage always occurs in one or two of the rows, it may be sufficient to monitor only those rows which are likely to suffer the most from fatigue. The groups 23 of sensors provide means for generating a displacement signal indicating displacement of an object, such as a turbine blade caused by vibration. The displacement signals produced by the groups 23 of sensors are supplied to signal conditioning circuitry 24 which removes identifiable noise and strengths the signals as necessary before the signals are supplied to a digitizer 26. The digitizer 26 performs analog/digital conversion to detect changes in the signals output by the groups 23 of sensors and provide digital data that can be processed by a data processing unit 28. The data processing unit 28 uses formulas and data stored in a data storage unit 30 to provide fatigue accumulation means for calculating fatigue usage in dependence upon the displacement signals. The fatigue usage is recorded in the data storage unit 30 and put out to an operator as messages 32. The data processing unit 28 performs several functions in order to calculate fatigue usage. First, it is necessary to identify which blade is being detected by a sensor. As described herein, this determination is made using a once-per-revolution signal supplied by a sensor 34. The position of each of the blades at the time the once-per-revolution signal is generated is known. The time between generations of adjacent once-per-revolution signals can be used to calculate the angular speed of the blades. The once-per-revolution signal is also used to determine the position of a blade. This is accomplished as illustrated in Fig. 3. Assuming one of the blades 12 is at position 36 when the once-per-revolution signal is received, it will be approaching sensor 18 at position 38 after having moved an angular displacement α. The time required for a turbine blade to move from position 36 to position 38 can be determined from the angular velocity . The data processing unit 28 is thus able to calculate an expected arrival time for each of the blades 12 at each of the sensors, e.g., 16-22, based upon the once-per-revolution signal. The difference between expected and actual arrival time is illustrated for a twenty-four (24) sensor per row system in Fig. 4A. The expected arrival time is indicated by dashed lines while the actual position of a rotor blade 12 at that time is indicated by a solid line. The sensor positions which correspond to the sensors illustrated in Fig. 1 have corresponding reference numerals in Fig. 4A. The rotor blade illustrated in Fig. 4A is oscillating approximately twice for every revolution of the turbine blades. As illustrated in Fig. 4A, the blade being monitored arrives at sensor 16 at the expected time. However, it arrives at sensors 17-19 before the expected time and at sensor 20 after the expected time. As is evident from Fig. 4A, sensors 18 and 20 respectively provide the maximum positive and negative displacements measured by the sensors. Approximately the same measurements are provided by the sensors opposite sensors 18 and 20 since the blade is vibrating at approximately twice the revolution speed of the turbine. If it was vibrating three times as fast as the rotation speed, there would be three each maximum positive and maximum negative displacements. The amount of displacement measured by each of the sensors is illustrated in Fig. 4B. The measurement made by sensor 18 is shown along the y-axis and the measurements of sensors 16 and 20 are indicated by reference numerals along the x-axis. The oscillatory nature of the vibration is more readily apparent from the graphical representation in Fig. 4B. As indicated in Fig. 5, blade position data 40 and steady state data 42 is used to calculate vibration and steady state stress in step 44. By using 24 sensors evenly spaced around the row of the turbine blades, the amplitude modulation and frequency modulation of vibration at frequencies up to twelve times the speed of the rotor shaft 10 (the twelfth harmonic) in dependence upon the displacement signals, can be determined. If necessary, the data processing unit 28 can interpolate between the detected points. All significant vibrations of turbine rotor blades are expected to occur below the twelfth harmonic. If fewer sensors are used, the higher frequency vibrations will be aliased within the detected range of frequencies. As a result, as few as two sensors can be used. However, additional signal processing in step 44 is required when few sensors are used. Two inspection ports, approximately 135° apart, are commonly provided on turbines used for electrical power generation. This permits two passive proximity probes, such as magnetic or capacitive proximity probes, or optical sensors to be installed and used during operation of the turbine. Sensors 16 and 20 are illustrated in Fig. 1 approximately 135° apart and thus are representative of a two sensor per row system for generating signals indicative of the proximity of the turbine blades to the probes. The two sensors 16 and 20, when used alone, are able to detect all vibrations at frequencies less than the frequency of rotation of the turbine. Thus, if the turbine is rotating at 3600 rpm, vibrations at frequencies less than 60 Hz can be detected. Higher frequencies can be detected as aliased signals. According to a preferred embodiment of the present invention, a Hilbert transform of the displacement signal which provides blade position data 40 is preferably used to determine the frequency and amplitude of the turbine blades. The Hilbert transform of a vibration signal v(t) is defined in equation (3). The magnitude or amplitude envelope of the signal v(t) is defined by equation (4). A(t) = |v(t)| = √ v(t)² + H(v(t))² (4) This corresponds to the amplitude envelope A(t) indicated by dashed lines in Fig. 6. The instantaneous frequency ϑ ˙ is defined by equation (5) where ϑ(t) is defined by equation (6). ϑ (t) = (1/2π)(dϑ(t)/dt) (5) ϑ(t) = arctan(H(v(t))/v(t)) (6) This technique is used to find the amplitude envelope A(t) and instantaneous frequency ϑ ˙(t). These are supplied together with the steady state stress S-S to step 46 so that fatigue usage can be accumulated in dependence upon the vibration of the turbine blades 12. The instantaneous frequency ϑ ˙(t) provides the value of F(t) and the amplitude A(t) can be converted to actual vibratory stress ε a (t) using data, generated in laboratory tests which correlates tip deflection and stress, that is stored in the data storage unit 30. Thus, all of the terms required in equation (1) to accumulate fatigue usage are available in step 46 so that fatigue usage can be generated in step 48. It should be noted that equation (1) assumes that the steady state stress ε m (t) and vibratory stress ε a (t) should be algebraically added to provide a conservative estimate of accumulated fatigue. Finite element analysis can be used to determine an appropriate manner to add vibratory and steady state stress if it is desired to more closely predict the fatigue life of the object being monitored. The present invention has been described primarily as applied to fatigue in turbine rotors. Similar types of objects to which the present invention could be applied include airfoils, propeller blades and the compressor section of jet engines. Also, fretting in steam generator tubes accumulates due to vibration in a manner similar to fatigue. Thus, the present invention could be applied to accumulating fretting of steam generator tubes by the use of appropriate sensors. In general, any force exhibiting a "bursty" signature, like that illustrated in Fig. 6 with sudden increases in amplitude for short periods of time, and causing damage which is cumulative may be monitored by assessing accumulated damage according to the present invention. IDENTIFICATION OF REFERENCE NUMERALS USED IN THE DRAWINGS LEGEND REF. NO. FIGURE SIGNAL CONDITIONING 24 2 DIGITIZER 26 2 DATA PROCESSING UNIT 28 2 DATA STORAGE 30 2 MESSAGES TO OPERATOR 32 2 BLADE POSITION DATA 40 5 STEADY STATE DATA 42 5 CALCULATE STEADY-STATE STRAIN & VIBRATION (BY HILBERT TRANSFORM) 44 5 ACCUMULATE FATIGUE USAGE 46 5 OUTPUT FATIGUE USAGE 48 5

Claims: A continuous measuring apparatus for measurement of accumulated mechanical fatigue of vibrating members (12) of a bladed turbine rotor so as to compute "fatigue usage" as a measure of accumulated fatigue to learn regarding a remaining life of the vibrating members (12) before fatigue breakdown, said apparatus comprising a rotor torque sensor, sensors (16, 22) mounted proximate to a vibrating member for generating a displacement signal indicating displacement of said vibrating members (12) caused by vibration of the member; and fatigue accumulation means (28, 30) for calculating "fatigue usage" in the member in dependence upon the displacement signal, characterized in that said fatigue accumulation means includes means subjecting the displacement signal generated by said sensors (16, 22) to a Hilbert transformation for determining frequency and amplitude of vibration of the turbine blades and means utilizing Goodman's law as applied to the frequency and amplitude of the vibration of the turbine blades with the addition of torque stress as determined by the rotor torque sensor to compute fatigue usage by accumulating fatigue of the turbine blades. An apparatus as recited in claim 1, characterized in that said sensors (12) are passive proximity probes (23) for generating signals indicative of proximity of the member to said passive proximity probes. An apparatus as recited in claim 1, characterized in that said sensors (12) comprise means for optically detecting the displacement of the member. An apparatus as recited in claim 1, wherein said vibrating members are the turbine blades, characterized in that said sensor means comprises at least two sensors positioned outside a path taken by the turbine blades. An apparatus as recited in claim 4, characterized in that approximately 24 vibration sensors are evenly spaced around a row of the turbine blades for detecting passage of said blades. An on-line fatigue measuring method for measuring fatigue of turbine blades in a turbine, having at least two vibration sensors positioned outside a row of the turbine blades for detecting passage of the turbine blades without contact therewith so as to produce sensor signals; and a torque sensor for sensing torque generating by the turbine characterized by the steps of: using Hilbert transformation for determining frequency and amplitude of vibration of the turbine blades from the sensor signals produced by said two sensors; and computing fatigue usage as an accumulation of fatigue of the turbine blades by application of Goodman's law to the frequency and the amplitude of the vibration of the turbine blades with the addition of steady stress on the turbine blades, the steady stress being determined in dependence upon the torque sensed by the torque sensor. A method as in claim 6, characterized in that two of said vibration sensors are arranged circumferentially around said blades and angularly spaced by 135°.

Inventors: KENDIG, ROBERT PAUL, LUCHETA, ROGER ANGELO, MCKENDREE, FRANCIS SPEED
Applicants: WESTINGHOUSE ELECTRIC CORPORATION
Application year: 1989
Main classification: G07C3
IPC codes: G07C3, G01N3, G01H1, G01M15, G01M19