Where next for Condition Monitoring?

Key Engineering Materials Vols. 245-246 (2003) pp 203-214 online at http://www.scientific.net © (2003)Citation Trans Tech Switzerland Journal (to bePublications, inserted by the publisher) Online available since 2003/Jul/15 Copyright by Trans Tech Publications

Where next for Condition Monitoring? A.W.Lees School of Engineering, University of Wales, Swansea, UK [email protected] Keywords: Condition Monitoring, Vibration, Rotating Machinery, Fault Diagnosis

Abstract Condition monitoring has progressed for many years with what may be termed incremental but substantial improvements to algorithms for data analysis. In tandem with this process has been increased understanding of machine operation by modelling. In this paper a discussion is given on recent work to tune models with plant data. More importantly, consideration will be given as to the information which can be established about an operational machine, and how this might be implemented in future condition monitoring systems to significantly enhance their value. Introduction The term Condition Monitoring has a wide variety of connotations ranging from a subjective judgement from relatively crude measurements to the use of advanced signal processing on plant data to form the basis of maintenance scheduling. It seems inevitable and certainly desirable, that the trend towards advanced signal processing will continue for high value equipment. The basic goal is clear; it is simply to gain the maximum information from the measurement data available. This begs the question of how much data is needed, a point that will be touched upon later. This paper offers a strategy for developing the topic. Types of Analysis In one sense, condition monitoring has always been with us. Engineers have always taken out of service machine which were exhibiting excessive noise and/or vibration or showing marked deterioration in performance. Work in the devcelopment of the subject has been aimed at the detection and diagnosis of incipient faults and the minimisation of false alarms. The increase in computing power has played an important role in developments [1,2]. Many operational parameters play a role in condition monitoring but at present there is some difficulty in merging operational information with the variations of vibration amplitudes under nominally steady running conditions, and indeed this is a feature of the inadequacy of the models currently in use. Two classification parameters are on line/offline and statistically [e.g. 3] based or physics based. Within each of these classification is a wide variety of experience. For a large turbop-alternator, the practice for many years has been to gather data during machine run-down. This data is rich in information as a number of resonances of the machine can be excited as the rotor traversss the appropriate speed range. In addition to these run-downs, there is on-load data. Since for many machines, as in the case of a power turbo-alternator, the operation is at constant speed, the data is not rich in information – but there is a lot of data. The simplest possible scheme would be classified as alarm triggering. Such a scheme would monitor on-line levels with a pre-set level that triggers an investigation, together with some higher level at which the machine in question would be removed from service. Most, if not all of the All rights reserved. No part of contents of this paper may be reproduced or transmitted in any form or by any means without the written permission of the publisher: Trans Tech Publications Ltd, Switzerland, www.ttp.net. (ID: 130.203.133.33-14/04/08,13:23:48)

204

Damage Assessment of Structures V

Title of Publication (to be inserted by the publisher)

published standards on vibration levels are based on this type of concept. The prescribed levels for different courses of action (i.e. investigate or abort) are based on a wealth of experience, albeit unspecific. For many years, in a process which continues today, investigators have sought refinement to this simple concept with the overall objective of accurately predicting incipient machine failure without excessive ‘false alarms’. The assessment of the state of rotating machinery has become progressively more quantitative over the past four decades. Engineers have sought to assess rotor unbance, bends, misalignment, rub and rotor cracks as early as possible. Whilst models have played an important role in a number of cases, there are still areas of discrepancy with measured data and these to a large extent centre on the uncertainties of the supporting structure. Several groups around the world have addressed this issue by employing various techniques of System Identification. This has some important implications for future condition monitoring approaches.

Basic method of identification The complete derivation of the method as presented in reference [4] is rather mathematical but the physical basis of the approach is straightforward. It is assumed that there exists a good mathematical model of the rotor, some less accurate description of the bearings, but little or nothing is known about the behaviour of the supporting structure. Such a scenario is common in the case of large turbo-generators whilst for smaller machine the formulation may be modified as appropriate. This is particularly easy if measurements are made of absolute shaft motion. However, the method is illustrated by reference to the large machine case with only bearing pedestal motion available. Although in principle the unbalance can arise anywhere along the rotor, it is known from modal theory that for any finite frequency range, the unbalance distribution can be represented by a set of unbalances at a finite number of pre-determined balance planes. Hence we may represent the ‘effective’ unbalance by a set of unbalance components in these planes. The motion of the rotor will be determined by two sets of forces namely the unbalance forces, and the forces generated by the bearings. Since the dynamic properties of the rotor are understood, and the response has been measured, it is possible to derive a relationship between the unbalance and the bearing forces. This can be show to be

m

F1 . -1 . = [a ] . Fn

k 1 y p1 - k 1 i =1

G1ei w 2 ei

. . .

m

k n y pn - k n i =1

(1) Gnei w 2 ei

where k n represents the stiffness of bearing n, y pn is the measured pedestal motion, G is a function which describes the dynamics of the rotor and may be considered as a dynamic flexibility of the rotor, and a is a matrix which depends on both bearing and rotor properties.

Key Engineering Materials Vols. 245-246

205

Note that the expression for the forces exerted on the rotor and the reaction on the bearing pedestal are a function of the bearing stiffnesses, but are independent of the foundation stiffness. The foundation will, of course, strongly influence, the pedestal vibration yp , but this is measured. A discussion of this approach and the conditioning of the matrix [a] has been given in [5]. Although the force and the balance have now been related to each other, neither is known, but the can be determined by considering the effect of the force on the supporting structure. Let the dynamic behaviour of the supporting structure be represented by the undetermined stiffness and mass matrices [K] and [M]. A damping matrix may also be introduced, but since the damping of rotating machinery is usually dominated by the behaviour of the bearing oil film (which is easily included in the analysis), the damping matrix may be neglected. Using these matrices, a further vector equation may be written to express the force vector as

{ }

{ }

-{ F } = [ K ] y p - w 2 [ M ] y p

(2)

and an equation is formed at each frequency measured. Note that equation (2) limits the number of modes in the foundation to equal the number of bearings. In the case of a foundation with many modes within the running frequency range, the structural matrices should vary. Combining 1 and 2 give an equation in whch the unknown parameters are the elements of the matrices K and M together with the unbalance components. Using measurements during a slow machine run-down, a large quantity of data is assembled and, in effect, equation 2 may be written. Equating the two force expressions at each frequency yields the equation

- [ w(w )] {v} = [ p(w )] { yr (w )} - [ q(w )] {e}

(3)

Assembling these equations at each measured frequency monitored, gives

[W ] { v} + [Q] { e} = { P}

(4)

In this equation (4), the matrix [W ] contains measured data, [Q] is based on the known model of the rotor, P has information of the bearing model, whilst the vector {v} is made up of the unknown matrix elements of the support stiffness, mass and damping, but in practice the support damping is rarely significant. The equation of motion of the rotor in a machine may be described [4] as Z R ,ii

Z R ,ib

0

Z R ,bi 0

Z R ,bb + Z B -Z B

-Z B ZB + ZF

rR ,i

fu

rR ,b = 0 rF ,b 0

(5)

where Z is the dynamic stiffness matrix, the subscripts b and i refer to internal and bearing (connection) degrees of freedom respectively, and the subscripts F, R, and B refer to the foundation, the rotor and the bearings. r are the responses and f u are the unbalance forces, which

206



are assumed to be applied only at the rotor internal degrees of freedom. The dynamic stiffness matrix of the foundation, Z F , is defined only at the degrees of freedom connecting the bearings and the foundation. In addition to the unbalance forces expressly shown in this equation, there will be static and dynamic forces applied at the bearings – but care is required to avoid “double accounting”. As written, equation (5) includes reaction to the unbalance forces, but it does not include static forces arising from bearing misalignment. As shown by Smart et al.[4], the matrix Z F , representing the foundation dynamic properties, is readily identified using least square techniques and similarly the unbalance vector e can be established, both using dat from a single rundown of the machine. It is well known that angular, or dynamic misalignment has the effect of inducing a bend into the rotor and this produces a vibrational excitation at synchronous speed which is subtly distinct from mass unbalance response. Edwards et al.[6] have presented a method for the identification of rotor bends. This involves expressing the bend geometry in terms of the free-free modes shapes of the rotor, and then modifying the term q in equation (3). The derivation of the static misalignment forces is a little less direct. Feng and Hahn[7] have studied the changes in alignment on a laboratory rig. Sinha et al[8] have recently reported an approach based on the identification of forces at couplings, but for large machines with rigidly coupled rotor, an alternative approach is approach based on the identification of bearing stiffnesses. Since the dynamic parameters of journal bearings is strongly influenced by the static load applied, a link can be established. This is illustrated in figure 1. Which shows the direct stiffness in on direction as a function of both rotor speed and static load.


207

Figure 1 Stiffness dependence on load and speed. Whilst this figure has been calculated using short bearing theory, (Hamrock, [9]) similar dependence is shown by more sophisticated models. Similarly, the damping terms are functions of load and speed as shown in figure 2. Using the know variation, the bearing loads can be identified in two ways. From equation write 1 Z F rF ,b + Z B P -1 Z R ,bi Z -R,ii fu = Z B P -1 Z B - I rF ,b

we

(6)

The bearing matrix Z B is a function of the static force, but this approach results in a non-linear estimation problem. An alternative procedure is to analyse the total residue for a range of static forces. Sinha et al, showed that estimates of bearing force were relatively poor, unless data is available of rotor position for each bearing. This greatly enhances the quality of the estimated parameters.

208



Figure 2 Variation of damping terms with load and speed

Sinha et al [8] have estimated bearing results from noisy simulated data and results are encouraging. Figue 3 shows an example of the agreement obtained when tuning the model to noisy data. Whilst some older turbo-generator units are not equipped with proximity probes,. This instrumentation is becoming standard on new equipment. Hence it has now been established that identified values are available for a) the foundation parameters b) the bearing loads c) the state of balance d) rotor bends The static deflected shape can now be expressed as

y r ( x ) = k r-1 mr g +

n

Fbi d (x - xi )

(7)

i =1

where k r , mr are the matrices associated with the rotor which are known from the initial model, g is a gravity vector, Fbi is the identified force at bearing i which is at axial location xi . The only problem here is that the matrix k r is singular. To remove this singularity, one approach is to specify the position of the end bearing pedestals. This, in essence, specifies the position and average gradient of the rotor in space. Even without this information, the stress profile of the rotor can be calculated.

Vertical Displ., m

Horizontal Displ., m


10

10

10 10

10

10

209

-4

-6

Simulated Initial Bearing Forces Non-Linearly Estimated Bearing Forces

-8

0

10

20

30

40

50

60

Frequency, Hz

-4

-6

Simulated Initial Bearing Forces Non-Linearly Estimated Bearing Forces

-8

0

10

20

30

40

50

60

Frequency, Hz Figue 3: Simuulated situatio with noisy data

Implementation

Although this procedure might appear to some fairly complex, it is purely algorithmic and in time can be readily automated. This would allow significant information gain following each machine rundown. This sequence is readily followed: 1. Rundown automatically processed as described above There is a rather modest overhead in doing this: the rotor model would need to be set up for each class of machines. i.e. On a power station with say four machines, there will probably be a single rotor model. This point has been discussed in several previous papers [4, 11]. The variations which exist between nominally identical machines are functions of their supporting structure and these differences can be treated. Ideally rotor models should be validated using a free-free test. 2. Estimated unbalance trended against previous values (classified among hot and cold rundowns) 3. Foundation parameters compared with previous values With the automated calculations, separate records could be assembled to monitor foundation parameters, state of balance, rotor bend, bearing (static) forces and hence alignment. 4. Alignment changes monitored 5. If proximity probe data is available on the unit the bearing characteristics may be inferred and may be indicative of wear within the bearing.

210



With a separate treatment, a full record of bearing properties can be assembled. This is again made possible by the derivation of the forces at the bearings by use of a good rotor model. Given such a system a great deal of insight into a machine’s condition can be gained with virtually no additional equipment or effort about that which is expended currently. Basic research has now developed techniques for the calculation of the parameters mentioned above, although there is still discussion among several research groups with regard to the most efficient methods. When these issues have been resolved significant software development will be required to implement these approaches. However, prototype schemes could be installed in the very near future. A further intriguing possibility arises: because after analysis we have full knowledge of the rotor’s position in the bearings and the unbalance forces, full information may be recovered using the model of the rotor to yield the deflected shape of the rotor thus highlighting any areas of rubbing.

Benefits

By pursuing this analysis, what is being done is at all times seeking to fit the observed behaviour and the numerical model. Regarding the model and the plant data as sources of information, a judicious combination of the two will yield the maximum information about the state of the plant. This idea may be surprising to some who might argue that the plant data is ‘real’ whilst the model is a mere figment of imagination. This however, is not the case.

Current status of work

The techniques described in this paper have now been extensively tested in simulation and tested on some simple rigs at Swansea. They have also been applied to a large rotating facility at Aston University. Results so far have very encouraging, but further work is needed. This was apparent in parts of the Aston work [10]: when rotor unbalance was estimated excellent values were obtained for the magnitude of the unbalance, but the phase showed significant error. This is believed to be be due the inadequate modelling of the bearings. Unbalance estimation was applied ‘blind’ to a 350 MW turbo-generator which had suffered a blade loss at a location not disclosed initially to UWS. As reported in [11],results were very encouraging for magnitude and axial location, but again the phase was in error. At the time of writing, a new laboratory rig is being assembled at Swansea comprising two rotors mounted on four journal bearings. The total length of the (38mm diameter) rotor is 3.5 meters and the system is driven via a flexible (membrane) coupling. The important features of the rig are 1) Each of the rotor has a flexural free-free mode within the running range 2) Pedestal motion is monitored in the two transverse directions 3) Shaft motion is measured in two directions at each bearing location 4) Two load cells are incorporated into each pedestal. 5) The data acquisition system has been designed with sufficient capacity to permit the monitoring of oil temperatures, room temperature and vibration at locations on the supporting structure. The facilities offer scope to allow significant progress in this area. A significant question to be resolved is that of the sensitivity of predictions to data errors and specifically to ‘dead’ channels, a situation which frequently arises on operational plant. Some work


211

[8] has mentioned this aspect but further work is required to more completely understand the interdependencies of the results and the input data. The dependence on the rotor model has been extensively studied [12].

Where Next – Smart Machines

The discussion has been towards the implementation of what we may loosely term IT to otherwise conventional machines. However the greatly enhanced knowledge of the underlying system is the natural route to pursue smart technology to the introduction of smart machines. It is, in the author’s view, somewhat fanciful to uniquely identify all machine faults. But it is eminently feasible to yield probabilities for different types of fault. Bachschmidt et al.[13] has presented some work it this area but further steps are feasible with refined plant models. This may be taken a step further with the introduction of actuators to apply forces to mitigate some effects of fault types. The most obvious form of this type is through the use of magnetic bearings introducing variable stiffness parameters within a control circuit. Other possibilities include piezoelectric actuators, pressurised bearings and magnetic dampers. Some of these technologies will, no doubt emerge at the smaller end of the machine range, but may be expected to play an increasing role.

Conclusions

Recent developments in the identification of machine parameters have been outlined. The use of a validated rotor model opens numerous possibilities for the understanding of machine behaviour, only some of which have been discussed in this paper. Rapid progress is now possible to give machine operators further insights.

Acknowledgements

The author is pleased the thank several colleagues over the past few years, in particular Prof.M.I.Friswell for many stimulating discussions, and Dr J.K.Sinha for his alignment studies. References

1.

2.

3. 4.

5.

W G R Davies, A W Lees, I W Mayes and J H Worsfold,Vibration Problems in Power Stations, I.Mech.E Conference "Vibrations in rotating machinery", Cambridge,September 1976. T H McCloskey and M L Adams, Troubleshooting power plant rotating machinery vibration problems usin computational techniques: case histories, I.Mech.E. Conference ‘Vibrations in Rotating Machinery, Bath, UK, 1992. C. Capdesus, M. Sidahmed and J.L.Lacoube, Cyclostationary processes: Application in gears faults early diagnosis, Mech. Sys. Sig. Proc.,14(3) ,371-385, 2000. M G Smart, M I Friswell and A W Lees, Estimating turbogenerator foundation parameters: model selection and regularization, Proc. R. Soc. Lond. A456,pp1583-1607, 2000. Lees, A.W. and M I Friswell, 1996, “Estimation of forces exerted on machine foundations”, International Conference Identification in engineering systems, pp 793-803, Swansea,UK, 1997.

212



6.

7.

8. 9. 10.

11.

12. 13.

S Edwards, A W Lees & M I Friswell, The identification of a rotor bend from vibration measurements, 16th International Modal Analysis Conference, Santa-Barbara, California, February 1998,1543-1549 Feng, N.S. and Hahn, E.J., “Experimental Identification of the pedestals in a rotorbearing-pedestal system”, IFToMM International Conference on Rotordynamics, Darmstadt, 1998. J K Sinha, A W Lees and M.I.Friswell, Static force estimation of the fluid bearings of a flexible rotating machine using run down responses, Submitted to J.Sound & Vib.,2003. B J Hamrock, Fundamentals of Fluid Film Lubrication, McGraw-Hill, Inc., NJ., 1994 J.Sinha, M I Friswell & A W Lees, The identification of the unbalance and the foundation model of a flexible rotating machine from a single run-down , Mech. Sys. Sig.Processiing, 16(2-3), ppp255-271, 2002. A W Lees, S Edwards, and M I Friswell, “The estimation of foundation parameters and unbalance”, ”, I.Mech.E. Conference, Vibrations in rotating machinery, Nottingham, pp31-44., 2000. J.K.Sinha, Health mnitoring techniques for rotating machinery, PhD thesis, University of Wales, Swansea, 2002 N.Bachscmid, P Pennacchi, A Vania, G A Zanetta and L Gregori, Case studies of fault identification in power plant large rotaring machinery, IFToMM International Conference on Rotordynamics, Sydney, 2002..