WO2008049167A1

WO2008049167A1 - Diagnostic system, method and apparatus for rotary machinery

Info

Publication number: WO2008049167A1
Application number: PCT/AU2007/001628
Authority: WO
Inventors: Ben Byrne; Ben Fletcher; Norman Remedios
Original assignee: SIGMA ENERGY SOLUTIONS Pty Ltd
Current assignee: SIGMA ENERGY SOLUTIONS Pty Ltd
Priority date: 2006-10-25
Filing date: 2007-10-25
Publication date: 2008-05-02
Anticipated expiration: 2009-04-25

Abstract

Diagnostic systems and methods for rotating machinery comprising a shaft in at least one bearing are disclosed. The system comprises at least one pair of orthogonally mounted proximity sensors for measuring a proximity of the shaft to the bearing, a processor coupled to the proximity sensors and an output device coupled to the processor. The processor extracts a mean position of the shaft and a dynamic path of the shaft in the bearing from signals received from the proximity sensors and models at least the mean position of the shaft in the bearing. The output device represents the measured mean position of the shaft, the measured dynamic path of the shaft and the modeled mean position of the shaft in combination in a single image.

Description

TITLE

DIAGNOSTIC SYSTEM, METHOD AND APPARATUS FOR ROTARY

MACHINERY

FIELD OF THE INVENTION

The present invention relates to a diagnostic system, method and apparatus for rotating machinery. In particular, but not exclusively, the present invention relates a diagnostic system, method and apparatus for rotating machinery with journal bearings, turbo machinery and the like.

BACKGROUND TO THE INVENTION

Rotating machinery used in industry, mining, power utilities and other applications needs to be carefully maintained to maximise efficiency, minimise downtime and reduce the likelihood of failure. Rotating machinery, such as fans, pumps, mills, rotating kilns, steam, gas and hydro generators and draglines typically found in such environments comprise a shaft that rotates in one or more bearings and the motion of the shaft within the bearing needs to be accurately aligned and monitored to enable problems or potential problems to be identified.

A known method of monitoring rotating machinery whilst in operation has limitations in terms of accuracy, but avoids the costly and inconvenient disadvantage of shutting down the machinery. An alternative known monitoring method is performed on the stationary machinery, which achieves more accurate results, but incurs the cost and inconvenience of shutting down the machinery.

One method of monitoring medium to large rotating machinery employs a proximity probe as a primary transducer and an accelerometer as a support transducer. Typically, such monitoring also utilises a pair of orthogonal proximity probes per bearing, which permits the extraction of different information from the DC and AC components of the signals from the proximity probes. The DC component provides the static position of the shaft centre in the bearing, which is the mean shaft position over several shaft revolutions. The AC component provides the dynamic path or orbit of the shaft centre within the bearing.

Conventionally, the DC and AC components are represented separately, examples of which are shown in the screenshots in FIGS 1 and 2. FIG 1 shows screenshots of mean shaft position, or shaft centre line (SCL) and FIG 2 shows screenshots of the dynamic path or orbit. However, in the Applicant's product, the DC and AC components are represented together in a combined visual display as shown in the screenshots in FIG 3. This is of vital importance in diagnostics because the alignment of the bearings can be assessed and quantified and changes made to the alignments with a high level of confidence. Also, an oil film in each bearing is the main force transmission path to the casings and pedestals of the rotating machinery. It is preferable to address a vibration problem at the source rather than address the effect.

Despite the benefits provided by the Applicant's product, it is desirable to provide improvements to the known diagnostic systems, methods and/or apparatus for rotating machinery in order to improve accuracy and/or efficiency and/or reduce the cost associated with providing such a service.

In this specification, the terms "comprises", "comprising" or similar terms are intended to mean a non-exclusive inclusion, such that a method, system or apparatus that comprises a list of elements does not include those elements solely, but may well include other elements not listed. SUMMARY OF THE INVENTION

In one form, although it need not be the only or indeed the broadest form, the invention resides in a diagnostic method for rotating machinery comprising a shaft in at least one bearing, said method including: measuring a mean position of the shaft in the at least one bearing; measuring a dynamic path of the shaft in the at least one bearing; modeling at least the mean position of the shaft in the at least one bearing; and representing the measured mean position of the shaft, the measured dynamic path of the shaft and the modeled mean position of the shaft in combination in a single image.

In another form, the invention resides in a diagnostic system for rotating machinery comprising a shaft in at least one bearing, said system comprising: at least one pair of orthogonally mounted proximity sensors for measuring a proximity of the shaft to the at least one bearing; a processor coupled to the at least one pair of proximity sensors for: a) extracting a mean position of the shaft in the at least one bearing and a dynamic path of the shaft in the at least one bearing from signals received from the proximity sensors; and b) modeling at least the mean position of the shaft in the at least one bearing; and an output device coupled to the processor for representing the measured mean position of the shaft, the measured dynamic path of the shaft and the modeled mean position of the shaft in combination in a single image. In a further form, the invention resides in diagnostic apparatus for rotating machinery comprising a shaft in at least one bearing, said apparatus comprising: computer readable program code components configured to cause measuring a mean position of the shaft in the at least one bearing; computer readable program code components configured to cause measuring a dynamic path of the shaft in the at least one bearing; computer readable program code components configured to cause modeling at least the mean position of the shaft in the at least one bearing; and computer readable program code components configured to cause representing the measured mean position of the shaft, the measured dynamic path of the shaft and the modeled mean position of the shaft in combination in a single image.

Suitably, modeling of at least the mean position of the shaft is performed using a transfer matrix method. Further features of the present invention will become apparent from the following detailed description.

BRIEF DESCRIPTION OF THE DRAWINGS

By way of example only, preferred embodiments of the invention will be described more fully hereinafter with reference to the accompanying drawings, wherein:

FIG 1 shows screenshots of a prior art diagnostic system;

FIG 2 shows more screenshots of the system referred to in FIG 1 ;

FIG 3 shows screenshots of another prior art diagnostic system; FIG 4 is a schematic representation of a diagnostic system according to an embodiment of the present invention;

FIG 5 is a flowchart illustrating a diagnostic method according to an embodiment of the present invention; FIG 6 is an end view of a shaft in a bearing and associated parameters;

FIG 6A illustrates a misalignment relationship between the parameters;

FIG 7 is a flowchart illustrating modelling of parameters of rotating machinery;

FIG 8 is a side view of rotating machinery in the form of a first turbo generator;

FIG 9 is a side view of rotating machinery in the form of a second turbo generator;

FIG 10 is an example of an image generated by the present invention;

FIG 11 is an example of time waveform image generated by the present invention;

FIG 12 is an example of an image of a spectrum generated by the present invention;

FIG 13 shows the modelled relationship between natural frequency and damping of a shaft of rotating machinery as a function of shaft speed; FIG 14 shows the modelled mode shape of a first critical speed of the shaft;

FIG 15 shows the measured response of the shaft in terms of phase lag and amplitude;

FIG 16 shows a comparison of measured and modelled responses of the shaft when weights are added to the shaft; FIGS 17-19 show comparisons of measured and modeled misalignments of the shaft;

FIG 20 shows a comparison of measured and modelled shaft positions for different lateral eccentricities at different speeds; FIG 21 shows a comparison of modelled and measured shaft positions for a horizontal misalignment at different speeds;

FIG 22 shows a comparison of modelled and measured shaft positions at different speeds after correction of the misalignment depicted in FIG 21;

FIG 23 show modelled results of natural frequency against shaft speed; and

FIG 24 show modelled results of modal damping against shaft speed.

DETAILED DESCRIPTION OF THE INVENTION Referring to FIG 4, according to embodiments of the present invention, there is provided a diagnostic system 10 for rotating machinery comprising a shaft 12 in at least one bearing 14. The rotating machinery can be of any type, such as, but not limited to, that found in industry, mining and power utilities. The system 10 comprises at least one pair of orthogonally mounted proximity sensors or probes 16 for measuring a proximity of the shaft 12 to the bearing 14. The shaft is cylindrical and the bearing can be circular or elliptical in cross section. Typically, multiple pairs of proximity sensors 16 are employed. For example, a 16 channel system can be used that employs six pairs of proximity sensors and which accommodates speed and load variables and two process variables. A processor 18 is coupled to the proximity sensors 16 via a signal conditioning amplifier 20 and an analogue-to digital converter (ADC) 22. An output device 23 is coupled to the processor 18 for display purposes and can be any suitable known display device, such as a monitor, LCD screen etc. The signals from the proximity sensors 16 are low-pass filtered by the signal conditioning amplifier 20 and parallel processed by the ADC 22 at a predetermined sampling rate.

According to one embodiment, the digitizing rate of the ADC 22 is 50 points per revolution of the shaft 12. Therefore, if the shaft is rotating at 2000rpm (33 rotations/s), the digitizing rate will be 2kHz. Each block of 512 digitized points per channel collected simultaneously is processed, displayed and updated every few seconds. In addition to this real time display of data, the data is stored for future analysis.

The processor 18 extracts a mean position of the shaft 12 in at least one bearing 14 and the dynamic path (or orbit) of the shaft 12 in at least one bearing 14 from signals received from the proximity sensors 16 via the signal conditioning amplifier 20 and the ADC 22. The processor also models at least the mean position of the shaft 12 in at least one bearing 14 and represents the measured mean position of the shaft, the measured dynamic path of the shaft and the modeled mean position of the shaft in combination in a single image on the output device 23. Hence, with reference to the flowchart in FIG 5, a diagnostic method 100 for rotating machinery in accordance with embodiments of the present invention includes the step 110 of measuring a mean position of the shaft 12 in at least one bearing 14 and the step 120 of measuring a dynamic path of the shaft 12 in at least one bearing 14. The method also includes the step 130 of modeling at least the mean position of the shaft 12 in at least one bearing 14. The method may also include the step 140 of modeling the dynamic path of the shaft 12 in at least one bearing 14. The method also includes the step 150 of representing the measured mean position of the shaft, the measured dynamic path of the shaft and the modeled mean position of the shaft in combination^' in a single image. The modeled dynamic path of the shaft 12 in at least one bearing 14 can also be displayed in the same image. Using the measured mean position of the shaft 12

in at least one bearing 14, the model parameters and Eqn. (1) referred to below, the value of lateral misalignment present is calculated and displayed.

Referring to FIG 6 illustrating a shaft 12 in a bearing 14 for the bearing load inclination, various parameters associated with this arrangement are as follows:

C = circular bearing radial clearance, used as a non-dimensionalisation factor β = load angle δ = ellipticity of an elliptic bearing ε_o= non-dimensional misalignment ε = non-dimensional eccentricity

Sj= ε₀ + ε difference between the actual bearing positions and the aligned shaft at the bearing locations

S_y= non-dimensional lateral misalignment in the y direction ε_z= non-dimensional lateral misalignment in the z direction φ = attitude angle

The reference configuration for lateral alignment is quasi-catenary, which is simply the state at which the determinate sub-systems, two bearings per shaft 12

(or rotor), reach static equilibrium. There are no shear forces and bending moments at the couplings, which only transmit torque. The actual misalignments are defined

as the difference between the reference configuration state and the actual state of the bearings 14. The non dimensional misalignment at each bearing can also be defined by Equation (1): ε_o = εi - ε Eqn. (1)

where ε₀ = misalignment, εi = input parameter, and ε = bearing eccentricity in the aligned state, which are all non dimensionalised by the circular bearing radial clearance C. In the examples described herein, εi is input rather than ε₀, as practical ε, data for machinery is more accessible. It is also assumed, that the foundation is rigid, a reasonable assumption for the machinery to which the analysis is applied. FIG 6A illustrates the relationship between the parameters ε₀, ε_f and ε, i.e. the misalignment relationships. It should be noted that ε₀ is speed dependent, whereas ε, is not.

The flowchart of the transfer matrix programs used in modeling the parameters of the rotating machinery is shown in FIG 7. The programs calculate the bearing coefficients, loads for misalignment and foundation conditions before performing predictions of dynamic behaviour. A detailed description of the transfer matrix software is disclosed by Feng, N. S. and Hahn E. J., "Vibration analysis software for turbomachinery", Proceedings 1^st International Power and Energy Conference (INT-PEC), Gippsland, November / December 1999, Paper 105, 10pp.

Examples of the present invention and the results will now be described with reference to FIGS 8-24 and Tables 1-29 appended to the detailed description. Modelling was performed in relation to, and measurements were taken from, rotating machinery in the form of a 350MW turbo generator 50 shown schematically in FIG 8 and rotating machinery in the form of a 460MW turbo generator 60 shown schematically in FIG 9.

With reference to FIG 8, the 350MW turbo generator 50 comprises a HP/IP turbine shaft 52, a LP turbine shaft 54, a generator shaft 56 and a collector shaft 58 with a rigid coupling between each shaft. HP/IP-LP coupling 53 joins turbine shafts 52 and 54 and LP-generator coupling 55 joins LP turbine shaft 54 and generator shaft 56. Turbo generator 50 is particularly amenable to misalignment studies because all the shafts, with the exclusion of the collector shaft 58, are supported by two bearings. Hence, the alignment state for this model is well defined. Each bearing is identified as Brg1 - Brg7. The first six bearings are all elliptical, with ellipticity, δ = 0.50, to provide significant stabilizing preload.

With reference to FIG 9, the 450MW turbo generator 60 is notably different due to its load sharing features and bearing profiles. Turbo generator 60 comprises five shafts in the form of HP turbine shaft 61 , IP turbine shaft 62, LP turbine shaft 63, generator shaft 64 and exciter shaft 65 and four couplings in the form of HP-IP coupling 66, IP-LP coupling 67, LP-generator coupling 68 and generator-exciter coupling 69. The turbo generator 60 has the HP and IP turbines separated by a rigid coupling, but only comprises six bearings for the five shafts The IP turbine has no bearings and the LP shaft only has one bearing. The bearings on this machine, identified as Brg1 - Brgδ, conform to a Type 1 Pocket Bearing and in essence are a combination of elliptical and circular profiles. This shared bearing system is not readily amenable for misalignment studies as the conventional definition of the quasi-catenary aligned state does not apply. FIG 10 shows an example of an image 68 generated by the present invention in which the measured mean position 70 of the shaft 12 and the measured dynamic path, or orbit 72, of the shaft 12 are represented on a single image. These results were for hot Bearing 2 at 3000 RPM with no load. Consequently, bearing clearances can be viewed and bearing alignments can be assessed in real time. The orthogonal positions of the proximity sensors 16 are also shown.

With reference to FIGS 11 and 12, a time waveform 74 and a spectrum 76 can also be shown on the same screen of the output device 23. The examples in FIGS 11 and 12 were generated from a shaft 12 rotating at 3000 rpm.

Following a major overhaul of the HP/IP turbine of 350MW turbo generator 50 shown in FIG 8, the turbo generator 50 was limited to a maximum speed of 1270 rpm during run up due to high shaft vibration levels of about 65 microns peak at Brg 2. The first critical speed of the shaft provided by the manufacturers is 2300 rpm, which is well removed from the maximum speed of 1270 rpm. The shaft was removed from its casing for a low speed balance, requiring about an equivalent of 500gms-m close to the middle of the shaft.

Modeling of the shaft 12 computed the first critical speed of the HP/IP shaft at 1475 rpm, as shown in FIG 13. FIG 13 shows the natural frequency and damping of the first HP/IP shaft mode as a function of speed of the shaft. The critical speed is where the speed curve intersects the natural frequency curve and this demonstrated good agreement with a value of 1400 rpm. FIG 14 shows the modeled mode shape of the first critical speed of the HP/IP shaft. The modeled mode shape is the dynamic shape of the rotors at the critical speed. FIG 15 shows the measured response of the HP/IP shaft in terms of phase lag (upper graph) and amplitude (lower graph) following the post-balance run up, which again illustrates good agreement between the modeled data and the measured data.

The model frequency response at bearing 2 was also computed by imposing low speed balance weights on the shaft 12 and a comparison of the measured and modeled responses is shown in FIG 16. In FIG 16, the amplitude on the left axis ranges from zero to the peak amplitude in microns. The peak amplitude occurred at 1430 rpm. The agreement is satisfactory, but importantly the comparison explains why the 1475 rpm mode was an issue during the run up. The difference between the modeled and measured data is due to modal damping - the physical system has about half the damping of the model for the mode in question.

A convenient and efficient method of studying the alignment of the shaft 12 is to examine the effect of misalignment on eccentricity, ε, and attitude angle, Φ, at every bearing. Using the model results of the present invention and the measured results from the data collection software, the comparisons shown in FIGS 17-19 were generated for three of the bearings, Brg2, Brg3 and Brg5 respectively. The lines in FIGS 17-19 represent the centre line path of the shaft 12 for three run ups from 0-3000 rpm and 2 run downs. FIGS 17-19 also show the calculated (circles) and measured (triangles) centre positions of the shaft 12 at 1000 rpm, 2000 rpm and 3000 rpm. It can be seen that there is good agreement between modeled and measured data for each of the three bearings. The attitude angles correspond well and the eccentricities, though not as good, are well within the bounds of misalignment and thermal effects. The model data in FIGS 17-19 are for a bearing layout having the same shape as the catenary shape of a stationary shaft, i.e. ε_y = 0.5 at all bearings. The reference position for the plots in FIGS 17-19 is the bottom of the bearing obtained in the practical case with the shaft and jacking oil pump stopped after a hot run down.

The sensitivity results are established by imposing horizontal and vertical misalignments at Brg2 and Brg5 of the 350MW turbo generator 50 shown in FIG 8 within the limits measured on the shaft during outages. The tabulated results, shown in Tables 1-28 are for vertical and horizontal misalignments at Brg2 and Brg5. Tables 1-3 show the results for the shaft in an aligned state. Tables 4-12 show the results for a vertically misaligned shaft. Tables 13-28 show the results for a horizontally misaligned shaft. The trends observed are close to what has been observed in practice on these shafts. It has been observed in practice, as with the model, that the shaft position within the bearings is only weakly sensitive to vertical misalignment. For example, Brg2 can be lower than Brg3 by as much as 0.6 mm and result only in a 10% change in eccentricity, ε, and attitude angle, Φ, from the aligned state. The same applies to Brg4 and Brg5 that have the second coupling in between. The sensitivity to horizontal misalignment on the other hand is high at both bearings and more so at Brg5, which is the front generator bearing. The results from these calculations for Brg5 are presented graphically in FIG 20. The lines in FIG 20 represent the centre line path of the shaft 12 for three run ups from 0-3000 rpm and 2 run downs. FIG 20 also shows the calculated (modeled) centre positions of the shaft 12 (circles) and the measured centre positions (triangles). The centre positions of the shaft 12 are shown at 1000 rpm, 2000 rpm and 3000 rpm for different lateral eccentricities of -561 μm, -281 μm, 0 μm, + 281 μm and +561 μm from left to right in FIG 20. A practical case of high misalignment at the front generator bearing Brg5 is illustrated in FIG 21 , which shows a comparison of the modeled (circles) and measured (triangles) data for a measured horizontal misalignment of 561 microns and a modeled horizontal misalignment of 450 microns. A comparison of the modeled (circles) and measured (triangles) data after correction of the misalignment is presented in FIG 22. The correspondence between the model results and the measured results is good when it is considered that the horizontal misalignment caused significant wear in the bearings, thus modifying the profile as a result. The model of the 460MW turbo generator 60 shown in FIG 9 was studied in detail because of its unique load sharing capabilities, its stiff foundation, and because the generator 60 experienced steam whirl in the higher load range. The critical speeds of the model corresponded very well with the measured critical speeds from hot run down data, which are represented in Table 29 and FIGS 23 and 24. These modes are all lightly damped - at 5% or less of critical, which is just marginally acceptable for a turbo generator. The low modal damping is expected as the five shafts have only six bearings.

Steam whirl on the 50Hz turbine manifested as an instability when the flow through the HP turbine exceeded a critical value and whilst the turbine was generating in excess of 260MW. The sub synchronous whirl frequency was amplitude dependent in the range 32.5Hz to 33Hz, generated in the HP turbine and identified as a forward mode from the orbits. Though the cause of the instability was identified as steam whirl, the cause of the steam whirl is uncertain. It could have been due to misalignment between the HP Turbine shaft and its casing or from damaged seals on the balance piston. Nevertheless, both sources require a lightly damped mode at the instability frequency of 33Hz. This mode is predicted by the model, as shown in Table 29 at 33.1 Hz and with negligible damping.

The combination of modeling with selected practical measurements from rotating machinery is a viable approach to diagnostics and condition monitoring. The agreement between theory and practice presented here is good and augurs well for future developments in this area. This is particularly true because the models used assumed linearity and a rigid foundation. The model alignment studies are particularly important as they add credence to the predictive benefits of shaft centre line monitoring and can save significant overhaul time. The shaft centre line locus is a suitable practical parameter for relating theory to practice and as an essential condition monitoring tool. The model approach also serves well as a diagnostic tool by identifying design and maintenance limitations which in turn resulted in steam whirl on a 460MW machine. According to some embodiments of the present invention, there is provided a diagnostic apparatus as shown in FIG 4 for rotating machinery comprising the shaft 12 in at least one bearing 14. The apparatus comprises the processor 18 operatively coupled to a storage medium in the form of a memory. The memory comprises a computer readable medium for storing computer readable program code components for performing the diagnostic method in accordance with the teachings of the present invention, at least some of which are selectively executed by the processor 18 and are configured to cause the execution of the embodiments of the present invention described herein. Hence, the apparatus comprises, for example, computer readable program code components configured to cause measuring a mean position of the shaft 12 in the at least one bearing 14 and computer readable program code components configured to cause measuring a dynamic path of the shaft 12 in the at least one bearing 14. The apparatus also comprises computer readable program code components configured to cause modeling at least the mean position of the shaft in the at least one bearing and computer readable program code components configured to cause representing the measured mean position of the shaft, the measured dynamic path of the shaft and the modeled mean position of the shaft in combination in a single image.

Hence, the system, method and apparatus of the present invention thus provide an improved diagnostic and conditioning system, method and apparatus for a wide variety of rotating machinery. The combination of modeled results and measured results provides access to both existing rotating machinery and rotating machinery in the commissioning stage in order to identify the root cause of vibration problems, such as misalignment and imbalance, and the corrective action required. Modeling evaluates the effects of bearing alignment changes and operating parameter changes on system stability and vibration response. The data collection/analysis software that links with the modeling results provides valuable information about the measured shaft performance at the bearings. The combination of the two components provides an efficient and valuable tool that yields significant cost benefits.

Throughout the specification the aim has been to describe the invention without limiting the invention to any one embodiment or specific collection of features. Persons skilled in the relevant art may realize variations from the specific embodiments that will nonetheless fall within the scope of the invention. TABLES 1-29 FOLLOW " Aligned" at ORPM;

'ey = 0.5 at Bearings 1 to 6 ez=0.θ at all bearings = 1-41 at Bearing 7

" Aligned ^« State TABLE 3 Vertical Misalignment- down 0>4 at Bearing 2 ey = 0.5 at Bearings 1,3,4,5,6 ez=0.0 at all bearings = 1.41 at Bearing 7 = 0.1 at Bearing 2

TABLE 6 Vertical misalignment at Bearing 2 down 0.4 Vertical Misalignment- down 0.5 at Bearing 2 ey = 0.5 at Bearings 1,3,4,5,6 ez-0.0 at all bearings = 1.41 at Bearing 7 = 0.0 at Bearing 2

TABLE 9 Vertical misalignment at Bearing 2 - down 0.5 Vertical Misalignment - up 0.25 at Bearing 2 ey = 0.5 at Bearings 1,3,4,5,6 ez=0.0 at all bearings = 1.41 at Bearing 7 = 0.75 at Bearing 2

TABLE 12 Vertical misalignment at Bearing 2 up 0.25 Horizontal Misalignment = +0.5 at Bearing 2 ey = 0.5 at Bearings 1,2,3,4,5,6 ez=0.0 at 1,3,4,5,6,7 = 1.41 at Bearing 7 ez=0.5 at Bearing 2

TABLE 13 Horizontal Misalignment at Bearing 2 (+0.5)

Horizontal Misalignment = +1.0 at Bearing 2 ey = 0.5 at Bearings 1,2,3,4,5,6 ez=0.0 at 1,3,4,5,6,7 - 1.41 at Bearing 7 ez=1.0 at Bearing 2

Horizontal Misalignment at Bearing 2 (+1.0)

TABLE 14 Horizontal Misalignment - -0.5 at Bearing 2

ey = 0.5 at Bearings 1,2,3,4,5,6 ez?=0.0 at 1,3,4,5,6,7 = 1.41 at Bearing 7 ez=M).5 at Bearing 2

TABLE 15 Horizontal Misalignment at Bearing 2 (-0.5)

Horizontal Misalignment = -1.0 at Bearing 2

ey = 0.5 at Bearings 1,2,3,4,5,6 ez=0.0 at 1,3,4,5,6,7 = 1.41 at Bearing 7 ez— 1.0 at Bearing 2

TABLE 16 Horizontal Misalignment = -0.S at Bearing S

ey = 0.5 at Bearings 1,2,3,4,5_» and 6 ez=0 at Bearings 1,2,3,4,6 & 7 ey = 1.41 at Bearing 7 ez= - 0.5 at Bearing 5

TABLE 19 Horizontal Misalignment at Bearing 5 ( -0.5) Horizontal Misalignment = -1.0 at Bearing 5

ey = 0.5 at Bearings 1,2,3,4,5, and 6 e*= 0 at Brgs 1,2,3,4,6,7 e_y = 1.41 at Bearing 7 ez= -1.0 at Bearing 5

TABLE 22 Horizontal Misalignment at Bearing 5 ( -1.0) Horizontal Misalignment = +0.5 at Bearing S

ey = 0.5 at Bearings 1,2,3,4,5, and 6 e*= O at Brgs. 1,2,3,4,6,7 ey = 1.41 at Bearing 7 ez= 0.5 at Bearing 5

TABLE 25__- Horizontal Misalignment at Bearing 5 ( +0.5) Horizontal Misalignment = +1.0 at Bearing 5

e_y — 0.5 at Bearings 1,2,3,4,5, and 6 fe~ 0 at Brgs 1,2,3,4,6,7 Cy = 1.41 at Bearing 7 ez=1.0 at Bearimg 5

TABLE 28 Horizontal Misalignment at Bearing 5 (+1.0)

Comparison of the Natural Frequencies - Model and Experimental, TABLE 29

Claims

CLAIMS:

1. A diagnostic method for rotating machinery comprising a shaft in at least one bearing, said method including: measuring a mean position of the shaft in the at least one bearing; measuring a dynamic path of the shaft in the at least one bearing; modeling at least the mean position of the shaft in the at least one bearing; and representing the measured mean position of the shaft, the measured dynamic path of the shaft and the modeled mean position of the shaft in combination in a single image.

2. The method of claim 1 , further including modeling the dynamic path of the shaft in the at least one bearing.

3. The method of claim 2, further including representing the modeled dynamic path of the shaft in the same image.

4. The method of claim 1 , further including calculating a lateral misalignment of the shaft in the at least one bearing on the basis of at least the measured mean position of the shaft and the modeled mean position of the shaft.

5. The method of claim 1 , further including modeling at least the mean position of the shaft using a transfer matrix method.

6. The method of claim 1 , further including representing the measured mean position, the measured dynamic path and the modeled mean position in real time.

7. A diagnostic system for rotating machinery comprising a shaft in at least one bearing, said system comprising: at least one pair of orthogonally mounted proximity sensors for measuring a proximity of the shaft to the at least one bearing; a processor coupled to the at least one pair of proximity sensors for: a) extracting a mean position of the shaft in the at least one bearing and a dynamic path of the shaft in the at least one bearing from signals received from the proximity sensors; and b) modeling at least the mean position of the shaft in the at least one bearing; and an output device coupled to the processor for representing the measured mean position of the shaft, the measured dynamic path of the shaft and the modeled mean position of the shaft in combination in a single image.

8. The system of claim 7, further including the processor modeling the dynamic path of the shaft in the at least one bearing.

9. The system of claim 8, further including the output device representing the modeled dynamic path of the shaft in the same image.

10. The system of claim 7, further including the processor calculating a lateral misalignment of the shaft in the at least one bearing on the basis of at least the measured mean position of the shaft and the modeled mean position of the shaft.

11. The system of claim 7, further including the processor modeling at least the mean position of the shaft using a transfer matrix method.

12. The system of claim 7, further including the processor modeling at least the mean position of the shaft using a transfer matrix method.

13. The system of claim 7, wherein the at least one bearing of the machinery is circular or elliptical.

14. A diagnostic apparatus for rotating machinery comprising a shaft in at least one bearing, said apparatus comprising: computer readable program code components configured to cause measuring a mean position of the shaft in the at least one bearing; computer readable program code components configured to cause measuring a dynamic path of the shaft in the at least one bearing; computer readable program code components configured to cause modeling at least the mean position of the shaft in the at least one bearing; and computer readable program code components configured to cause representing the measured mean position of the shaft, the measured dynamic path of the shaft and the modeled mean position of the shaft in combination in a single image.

15. The diagnostic apparatus of claim 14, further comprising computer readable program code components configured to cause modeling the dynamic path of the shaft in the at least one bearing.

16. The diagnostic apparatus of claim 14, further comprising computer readable program code components configured to cause representing the modeled dynamic path of the shaft in the same image.

17. The diagnostic apparatus of claim 14, further comprising computer readable program code components configured to cause calculating a lateral misalignment of the shaft in the at least one bearing on the basis of at least the measured mean position of the shaft and the modeled mean position of the shaft.

18. The diagnostic apparatus of claim 14, further comprising computer readable program code components configured to cause modeling at least the mean position of the shaft using a transfer matrix method.

19. The diagnostic apparatus of claim 14, further comprising computer readable program code components configured to cause representing the measured mean position, the measured dynamic path and the modeled mean position in real time.