Abstract:
A vibration phasor monitoring system for real time determination of a vibration phasor magnitude and angle including a quadrature detector, implemented in software or hardware, whose reference phasors are locked in phase, via hardware, to a physical reference point on a rotating shaft. A vibration transducer and a transducer that senses a complete revolution of the shaft are disposed around the shaft. The transducers may be axially separated along the shaft. A clocking arrangement is implemented to determine the shaft angle at the time an output of the vibration transducer is read. Thereafter, the sine and cosine of the determined shaft angle are obtained and are used to multiply the vibration transducer output reading thereby resulting in respective projections of the vibration phasor on the sine and cosine reference phasors. These projections are then manipulated to obtain the vibration phasor angle and magnitude. Harmonic analysis in easily implemented by multiplying the generated shaft angle.

Description:
BACKGROUND 
     The invention relates generally to monitoring a rotating member. More particularly, the invention relates to an apparatus and method for monitoring in real time a vibration phasor at the fundamental frequency of a rotating shaft to determine, for example, whether such vibration is within a prescribed limit or range. 
     Electrical generating equipment, which often includes a rotating member, is often relied upon for mission critical tasks where a failure thereof can lead to increased expense or possible catastrophic effects, including machinery breakdown or even bodily injury. Thus, it is desirable to monitor this equipment in an effort to prevent such failures. Specifically, turbines are often brought up to or down from operating speed in stepped intervals to, for example, reduce thermal stress on the equipment. However, a rotating machine has natural resonant frequencies, which frequencies sometimes coincide with frequencies generated during the acceleration or deceleration process. To reduce damage to the machinery, it is desirable that these points of resonance be avoided to the extent possible during the speeding up or slowing process. 
     Monitoring of rotating machinery, and electrical generating equipment in particular, can be accomplished by monitoring changes in both magnitude and angle (relative to an index point on a shaft, for example) of a vibration phasor or vector. Changes outside acceptable limits can be reason to trip or halt the machinery to avoid damage or avoid further damage from occurring. Alternatively, data indicative of changes outside the acceptable limits could be used by a control algorithm to operate differently and thereby restore vibration to a within acceptable limits. Significantly, changes in magnitude and/or angle may occur rapidly such as when the machinery incurs a structural failure. Rapid vibration changes may occur as a turbine&#39;s rotating frequency passes through resonant frequencies. Vibration phasor changes may also occur slowly as the result of expected or unintended component wear. Since there is the possibility that the changes may be rapid, it is desirable, for protection to be effective, that the magnitude and angle of the vibration phasor be determined continuously in real time. 
     In General Electric&#39;s prior art rotating member vibration phasor monitoring methods, vibration phasor magnitude and angle are determined by post-processing via Fourier analysis of an array of readings obtained from a displacement transducer. However, the delay caused by the accumulation of the readings and data transfer from the input and output (I/O) card to, for example, a personal computer-based human machine interface for subsequent processing results in magnitude and angle updates too slow for protection from or control of rapid vibration changes and thus this method is suitable, at best, only for trending to monitor component wear. A system based on Fourier analysis is in use in, for example, General Electric&#39;s Speedtronic Mark V turbine controller. 
     Another vibration monitoring technique is described in U.S. Pat. No. 3,220,247 to Goodman, which is directed to detecting vibration in marine propulsion equipment. In Goodman, sine and cosine generators are provided which generate reference signals with reference periods which are the same as the periods of an unbalance signal. The unbalance signals and reference signals are coupled to multipliers and the resulting products are passed through filtering circuits to obtain average or mean values. In Goodman, a physical connection of a tachometer-generator to a rotating shaft is necessary. Such a connection, however, may be complicated and therefore costly. Furthermore, the tachometer-generator is subject to mechanical wear and might require that the machinery being monitored be shut down in the case of its failure, even though the machinery itself is experiencing no malfunction. Such unnecessary shutdowns can be extremely expensive for power plant operators and others. Further still, the 90 degree quadrature relationship of the sine and cosine references from the tachometer-generator is critical to the accuracy of any calculations. Unfortunately the 90 degree relationship relies on manufacturing tolerances in placing the respective windings of the tachometer-generator at 90 degrees from each other. Also, Goodman&#39;s device does not supply the vibration phasor angle in a form usable for automatic protection or control. The data is only available for display via an oscilloscope. Even the displayed data provides only a crude means of visually determining the angle. Additionally, the reference point on the rotating shaft to which the phasor angle is measured in Goodman is that point in shaft rotation that results in the tachometer-generator&#39;s sine output equal to 0 and cosine output equal to 1. If the coupling of the tachometer-generator to the shaft slips, the reference point on the shaft slips, i.e., moves as well. Finally, examination of harmonic vibrations in Goodman&#39;s apparatus would require a gear box or a multiple winding tachometer-generator, which adds yet further complications and expense. 
     Another vibration monitoring technique is described in U.S. Pat. No. 4,015,480 to Giers, which is directed to instantaneous measurement of unbalance. This apparatus includes the multiplication of the sine and cosine components of a reference phasor with multiple readings of vibration magnitude. Giers&#39; apparatus, however, is also deficient in a number ways. The apparatus requires physical connection of the clock generator, or in the case of a physical reference generator, both the reference and clock generator, to the rotating shaft. Such a connection may be difficult to accomplish and therefore undesirable. Further, Giers&#39; sampling frequency is dependent on the number of holes on the outer circumference of the disk in the clock generator. A high sampling frequency as desired for accurate and high resolution calculation of the phasor magnitude and angle would require an ever larger disk with more holes, which could become unmanageable. Further still, Giers&#39; apparatus requires synchronization of the reference and clock generators and compensates for less than perfect synchronization by increasing the sampling frequency. However, sampling frequency is limited to the number of holes as discussed above. 
     Further still, consistent and accurate sampling frequency and period in Giers depends on accurate placement of the holes in the disk of his clock generator. This requires precision manufacturing techniques. Also, as with Goodman, examination of harmonic vibrations would require a gear box. 
     Thus there is a need for a simple, real-time method and apparatus for accurately and effectively monitoring a vibration phasor in a rotating member for effective monitoring and control. 
     SUMMARY OF THE PREFERRED EMBODIMENTS 
     Therefore, it is intended to provide, by the apparatus and method described herein, in real time a vibration phasor magnitude and angle with respect to a reference point on a rotating member, preferably a shaft of a rotating machine such as a prime mover of an electrical generator, e.g., a gas or steam turbine. Producing such parameters of vibration with accuracy provides the advantage of applying beneficial protection to machinery that may experience structural failure or component wear. For instance, such machinery may be “tripped” or halted in a timely fashion, thereby avoiding damage or additional damage. Alternatively, the parameters of vibration may be used by a controller system to move the operating point of the machine in such a fashion as to reduce vibration to a rated level. The preferred embodiment effectively provides the vibration parameters in real time via a simple, cost effective, robust and flexible design. 
     More particularly, a quadrature detector, implemented in software or hardware, whose reference phasors are locked in phase, via hardware, to a physical reference point on a rotating shaft is used for real time determination of a vibration phasor magnitude and angle. A displacement transducer sensing vibration and a displacement transducer that senses a complete revolution of the shaft are disposed around a shaft. The transducers may also be axially and/or circumferentially separated along the shaft. A clocking arrangement is implemented to determine the shaft angle at the time an output of the vibration transducer is read. 
     Thereafter, the sine and cosine of the determined shaft angle are obtained and are used to multiply the vibration transducer output reading thereby resulting in respective projections of the vibration phasor on the unity amplitude sine and cosine reference phasors. These projections are then manipulated to obtain the vibration phasor angle and magnitude. 
     Thus, for each single reading of the vibration transducer the invention will yield both a new vibration phasor magnitude and new angle resulting in a true real-time measurement of vibration in a rotating member. 
     And, unlike the devices described by Goodman and Giers, no physical connection to the shaft of the machine is necessary, perfect quadrature of reference phasors is provided, accurate and usable vibration phasor magnitude and angle information is immediately available and analysis of harmonics is easily implemented. 
    
    
     BRIEF DESCRIPTION OF THE DRAWINGS 
     FIGS. 1-3 schematically illustrate a vibration phasor detection system in accordance with a preferred embodiment. 
     FIGS. 4A and 4B graphically depict the output of a transducer monitoring a milled slot or milled pedestal serving as a key of a rotating member in accordance with a preferred embodiment. 
     FIG. 5 graphically depicts the output of a displacement transducer for vibration associated with the rotating member in accordance with a preferred embodiment. 
     FIG. 6 illustrates a possible relationship among a vibration phasor and a quadrature pair of unity reference phasors. 
    
    
     DETAILED DESCRIPTION 
     Reference is now made to the figures for a more detailed description of the preferred embodiment. FIG. 1 shows a rotating member  10 , in this case a shaft of a turbine for example, having a vibration component  12  at the fundamental frequency of shaft rotation when shaft  10  is rotating. Of course, the shaft described herein can be associated with any type of rotating machinery. Two displacement transducers  16 ,  18  are disposed around in close proximity to, but not in contact with, the shaft  10 . Transducer  16  monitors the presence of a key or milled slot  14  disposed on shaft  10  and preferably is placed such that it will respond to displacement, i.e., distance changes with the passing of the key  14 . Alternatively, transducer  16  could monitor a milled pedestal as opposed to the aforementioned milled slot. FIGS. 4A and 4B depict typical voltage signals  400 ,  405  output from transducer  16  upon passing of a milled slot or milled pedestal. Transducer  18 , on the other hand, is a displacement transducer for measuring vibration. Transducer  18  may be placed axially anywhere along shaft  10  where it is desired to determine a vibration phasor  12 . FIG. 5 illustrates a typical voltage signal  500  output from transducer  18  when a vibration, i.e., displacement, is sensed by the transducer  18 . As can be understood by inspecting FIGS. 4A,  4 B and  5 , transducers  16 ,  18  each produce an output voltage proportional to the distance between the transducer face and the rotating shaft  10 . The D.C. component of these voltages is proportional to the distance between the transducer with the shaft  10  at rest (assuming negligible shaft run out). This distance is sometimes referred to as the gap or air gap between the transducer  16  or  18  and shaft  10 . The dynamic or A.C. component of the voltage signals  400 ,  405  or  500  shown in FIGS. 4A,  4 B and  5 , respectively, is proportional to the increasing or decreasing distance due to vibration or, in the case of the key transducer  16 , the passing of the key  14 . It is noted that the angular relationship between transducers  16 ,  18  is not critical and can be set as desired as this relationship does not affect properly calculating the angle of the vibration phasor. 
     As shown in FIG. 1, signal conditioning circuitry is preferably provided to process the voltage signal  400  or  405  that is output from transducer  16 . Specifically, it is, in accordance with the preferred embodiment, desired to create a logic signal  26  momentarily TRUE when the key  14  passes transducer  16 , and FALSE otherwise. This is accomplished with a voltage comparator  20  and edge detector  22  combination, preferably with hysteresis, that compares the output of transducer  16  against a predetermined level  30  which defines the threshold for a key passing event. The predetermined comparison level  30  is preferably set via software (although it could be hard wired), communicated via bus  28  and is converted to an analog signal in D/A converter  24 . The output of comparator/edge detector  20 ,  22  combination, preferably triggered on the falling edge of signals  400  or  405 , produces logic signal  26  indicating “key at 0 degrees” when TRUE. 
     FIG. 2 depicts a field programmable gate array  40  that provides much of the remaining signal conditioning functionality according to the preferred embodiment. Of course, it will be understood by those of ordinary skill in the art that the functions carried out by the field programmable gate array (FPGA)  40  may be carried out with discrete components, entirely in software or some combination thereof, depending on implementation circumstances. In FPGA  40  an oscillator  42  is used to feed a counter  44 . The frequency of the oscillator  42  and the bit width of counter  44  are chosen in view of the accuracy to which vibration phasor magnitude and angular measurement are desired. For example, in the preferred embodiment, a 6.25 megahertz oscillator  42  is implemented to feed a 24 bit counter  44  for use in an electrical power generating turbine spinning up to 18,000 rpm, or at a 300 Hz shaft speed. However, as noted, any clock or oscillator speed and counter size may be chosen depending on the particular application. The contents of counter  44  is, upon receipt of either of two independent enabling signals  26  (“key at 0 degrees” logic signal) or  34 , transferred via transfer blocks  46 ,  48  to one or the other of two latch registers  50 ,  52 . 
     More specifically, the transfer of the count in counter  44  to latch register  50  preferably is enabled when signal  26  is TRUE, i.e., a key phasor interrupt signal occurs. Additionally, once the transfer to latch register  50  has been completed, counter  44  is reset to zero. This reset avoids having to compute a delta count and/or having to compensate for counter rollover. Thus, latch register  50  contains the number of 6.25 MHz pulses that the oscillator  42  has produced during the time that has elapsed between successive occurrences of the key  14  passing transducer  16 . Accordingly, the count in latch register  50  represents a period measurement of to successive key passings of transducer  16  in terms of 6.25 MHz ticks. 
     The transfer of the count of counter  44  to latch register  52  is preferably enabled in response to a read request line  34  that is also connected to A/D converter  62  associated with the output  32  of transducer  18 . Operation of read request line  34  is preferably controlled by a microprocessor (not shown), which initiates in a periodic manner a reading at a preferred frequency of 1322.75 Hz of the output of transducer  18 . The digitized read value is shown as  64  in FIGS. 2 and 3. No resetting of the counter  44  occurs at the time of transfer to latch register  52 . Latch register  52  therefore contains the number of 6.25 MHz pulses or ticks that the oscillator  42  has produced from the time of the last key phasor reset occurrence, i.e., “key at 0 degrees” logic signal  26 , until the reading of A/D converter  62  occurs. Note that block  60  in FIG. 2 removes the D.C. component of the vibration measurement, i.e., any offset caused by the gap. 
     The significance of the latch registers  50 ,  52  lies in the ratio of the contents  58  of latch register  52  divided by the contents  54  of latch register  50 . This ratio, as shown in FIG. 3, is determined via divider or ratio block  70  at the time of processing the vibration reading  64 . The ratio or value output from block  70  represents the fractional part of complete a shaft revolution relative to the key phasor that occurred at the instant the vibration reading takes place. This fractional part of a revolution is multiplied by 360 degrees in multiplier  72  and becomes the shaft angle from transducer  16  (0 degrees) at the time of reading the output of transducer  18 , which reading is shown as  64  in the drawings. The shaft angle obtained from multiplier  72  is also shown graphically in FIG. 6 as element  113 , which is also, as explained below, the angle of one of a quadrature pair of unity phasors phase locked to the key  14 . 
     FIG. 3 further shows the implementation of a phase locked quadrature detector in accordance with the preferred embodiment and FIG. 6 illustrates graphically a possible relationship of the vibration phasor to the quadrature pair of unity reference phasors. The angle output from multiplier  72  is used to establish a quadrature pair of unity phasors. A unity cosine reference phasor  110  obtained via cosine block  74  represents a phasor in phase with the slot or key  14 . A unity sine reference phasor  112  obtained via block  76  represents a phasor lagging the key phasor by 90 degrees. By 90 degrees lagging, it is meant that this phasor is 90 degrees backward from the milled slot or milled pedestal serving as key  14  in terms of the direction of shaft rotation. 
     Using the unity reference phasors thus obtained, quadrature detection on the reading of the vibration phasor  114  whose instantaneous magnitude at the time of sampling is measured via A/D converter  62  is performed. That is, in accordance with the preferred embodiment, signal  64  is multiplied by each of the unity reference phasors. Each of these multiplications results in a composite signal. An “A.C.” portion of the composite is a sinusoid at twice the frequency of the shaft. A “D.C.” portion of the composite signal is half the projection of the vibration phasor upon the unity reference phasor it was multiplied by. A mathematical analysis of phasor multiplications is set forth below. 
     To extract just the projections, a low pass filter  84  or  86  is applied to each of products output by multipliers  78 ,  80 . The filters&#39; cutoff frequency and order are chosen to provide the desired response for the magnitude and angle determination while minimizing any ripple in these outputs. For example, in a preferred implementation, sixth order low pass filters with a cutoff frequency of 0.25 Hz are used. This filtering results in essentially having resolved the vibration phasor into its projections onto the two unity quadrature phasors  110 ,  112 , one of which (phasor  110 ) is in phase with the milled slot or key  14 . The projection magnitudes are half of what they should be (see the mathematical analysis), but this is dealt with as explained below. 
     Thus, to determine magnitude and angle of the vibration phasor  114 , the remaining functionality shown in FIG. 3 is implemented. Specifically, the outputs of low pass filters  84 ,  86  are squared in squaring blocks  88 ,  90  and added together in summing block  92 . The square root of the resulting sum obtained via square root function  94  is half the magnitude of the vibration phasor  114  and is therefore multiplied by 2 in multiplier block  96 . The angle between the vibration phasor  114  and the cosine reference phasor is the same as the angle between the vibration phasor  114  and the milled slot or key  14 . To obtain this angle, the arccosine of half the vibration phasor&#39;s projection on the unity cosine reference phasor  110  divided by half the magnitude of the vibration phasor  114  is determined via blocks  100  and  102 . The quantity one half the vibration phasor&#39;s projection on the unity cosine reference phasor is available from the output of the low pass filter  84 , for example, and the quantity one half the vibration phasor magnitude is available from the square root of the sum of the squares of the low pass filter outputs, i.e., the output of square root function block  94 . Accordingly, both the vibration phasor magnitude  98  and vibration phasor angle  104  are available in real time. As such, the magnitude and/or angle of the vibration phasor can be compared to threshold values, which, if exceeded, can be used to initiate the tripping or halting of the rotating machinery thereby avoiding damage or additional damage from occurring. 
     In order to study harmonics of shaft vibration multiplier  120  is provided between the output of multiplier  72  and cosine and sine blocks  74 ,  76 . To analyze the fundamental frequency of vibration, the input to multiplier  120  is set to 1. On the other hand, analysis of the harmonic components of any vibration can be studied by inputting a 2 or higher value into multiplier  120 . Thus, by simply changing the multiplier value input to multiplier  120  harmonic analysis can be effected. 
     Further, the vibration phasor magnitude  98  and vibration phasor angle  104  are preferably input to a control block  130  that monitors the magnitude and angle and responds in a desired fashion if either or both of these values are deemed to be outside of acceptable limits or beyond a rated value. In response to such conditions, control block  130  can initiate equipment speed control and/or shutdown, for example. Control block  130  preferably also includes readouts  132   a ,  132   b  for the vibration phasor magnitude and angle. 
     The following analysis provides a mathematical basis for the circuitry and method in accordance with the preferred embodiment. 
     MATHEMATICAL ANALYSIS 
     Multiplication of the vibration phasor by either reference phasor is governed by the following equation. 
     
       
         [ A   vib  SIN(ω vib   t +φ vib )][ A   ref  SIN(ω ref   t +φ ref )]= 
       
     
     
       
         [ A   vib   A   ref /2)COS((ω vib   t +φ vib )−(ω ref   t +φ ref ))]− 
       
     
     
       
         [ A   vib   A   ref /2)COS((ω vib   t +φ vib )+(ω ref   t +φ ref )]  (Eq. 1) 
       
     
     For the two phasors at the same frequency, i.e., ω=ω vib =ω ref  then equation 1 becomes: 
      [ A   in  SIN(ω vib   t +φ vib )][ A   ref  SIN(ω ref   t +φ ref )]=[( A   vib   A   ref /2)COS(φ vib −φ ref )]−[( A   vib   A   ref /2)COS(2ω t+φ   vib +φ ref )]  (Eq. 2) 
     From this it is observed there is a D.C. term, i.e. the first bracket as well as an A.C. term, i.e. the second bracket. The D.C. term is present only when the two phasors are at the same frequency. If equation 2 is passed through a low pass filter to remove the A.C. component while passing the D.C. component, equation 2 will simplify as follows: 
     
       
         Filtered{[ A   vib  SIN(ω vib   t+φvib )][ A   ref  SIN(ω ref   t+φ   ref )]}=[( A   vib   A   ref /2)COS(φ vib −  ref )]  (Eq. 3) 
       
     
     If the reference phasor is chosen to be a unity phasor, i.e. A ref ≡1, equation 3 further simplifies to: 
     
       
         Filtered {[ A   vib  SIN(ω vib   t +φ vib )][ A   ref  SIN ω ref   t +φ ref )]}=[( A   vib /2)COS(φ vib −φ ref )]  (Eq. 4) 
       
     
     It is now helpful to refer to FIG.  6 . 
     By definition 
     
       
         COS(φ vib −φ ref )≡(adjacent/hypotenuse )=(projection of  A   vib  onto  A   ref )/ A   vib   (Eq. 5) 
       
     
     Solving equation 5 for the term (projection of A vib  onto A ref ) yields 
     
       
         (projection of A vib  onto A ref )=A vib  COS(φ vib −φ ref )  (Eq. 6) 
       
     
     Comparing equation 6 to equation 4, it is apparent that: 
     
       
         Filtered{[ A   vib  SIN(ω vib   t+φ   vib )][ A   ref  SIN(ω ref   t+φ   ref )]}=(projection of A vib  onto A ref )/2  (Eq. 7) 
       
     
     In other words the filter output is one half the projection of the vibration phasor onto the reference phasor. 
     Thus, in accordance with the preferred embodiment, a real-time vibration phasor monitoring system is provided that quickly and accurately measures both the magnitude and angle of a vibration phasor of a rotating member. 
     While the foregoing description includes numerous details and specifics, it is to be understood that these are provided for purposes of explanation only, and are not intended to limit the scope of the invention. Those of ordinary skill in the art will easily be able to make numerous modifications to the exemplary embodiments described above without departing from the scope of the invention, as defined by the following claims and their legal equivalents.