An aeroengine monitoring (see also volume 1, chapter 4.2) can take place in different ways. In
this chapter 25.2.1, online procedures are described more in detail. In chapter 25.2.2 the use of
discontinous non destructive testing
methods (NDT) in the maintenance is shown with examples.
Typical continuous monitoring procedures are:
Obviously especially aeroengines of coming fighters should be equipped with hundreds of
sondes/probes. So the monitoring, respectively problem identification (Fig. "Model based diagnosis") of all important
components should be enabled. Here the success may especially depend from the success to consider
faulty measurements and drop outs of the sondes suitably (chapter 19.2.1).
Fig. "Health monitorin to search faults and failures": Basically we should be clear in our mind about the
requirements of a successful health monitoring for the identification of problems/failures in
time. Only for a small fraction of incidents it can be reckoned with success. This is true for continuous and discontinuous monitoring.
Also at low frequency loads like thermal fatigue of changes of centrifugal
forces (start-stop-cycles) in the LCF region, the remaining „reaction time“ can be short. This may be the case, if the
stress level is very high (volume 3, Ill. 12.2-10). Then
the crack growth is also very high. With this, the
critical crack length up to the residual fracture/forced fracture is short. Corresponding low is the number
of cycles up to the fracture/burst (diagramm right).
Also the stress gradient in the direction of the grack growth (sketch left) has an influence (volume 3, Ill. 18.104.22.168-18). If it is high, i.e. the tensile stress drops fast, the crack propagation can decelerate to stand still. This improves the „controllability”. This is for example true for so called rim cracks in (casted) integral turbine wheels (sketch left, Ill. 12.6.2-12). However, is the stress gradient like for hub cracks low, a not controllable accelerated crack growth must be expected.
Occurs a spontaneous crack and/or fast crack growth under the influence of corrosion (stress corrosion cracking, volume 1, Ill. 22.214.171.124-1) or hydrogen embrittlement (volume 1, Ill. 126.96.36.199-2), the spontaneous brittle fracture prevents a successful monitoring.
Even during static load, with usually sufficient slow deteriorating mechanism (creep), special influences can prevent a successful monitoring. Typical examples are, to the stress corrosion cracking related effects, like sudden crack formation through melted metals (e.g., silver, volume 3, Ill. 12.4-14 and volume 4, Ill. 188.8.131.52-10.1) or sulfur containing media (e.g., MoS2 , Fig. "Approved lubrication media" and 22.4.1-8) at hot parts, which underlie sufficient high tensile stresses.
-Thresholds of safe component behavior: Not until there is the knowledge about the time lapses, the concept of monitoring problems/failures enables safe inspection intervals. For this, it is necessary to know the monitoring relevant failure degree, respectively to define it. For cracks mostly the length may be concerned. Thereby the crack propagation must be considered (see section `failure propagation'). However, also the the result of a crack formation could be limited. An example are the breakouts at turbine guide vanes/nozzles. Here breakouts at the blade lead to flow disturbance (Fig. "Thermal fatigue cracks in turbine vanes") or to a hot gas entrance into the cooling system. During the definition of the limits; also dangerously changes of the component properties must be considered. This can be a larger elastic flexibility. It changes with a drop of natural fequencies resonances. This can promote high frequency vibrations (e.g., disc vibrations). The largest flexiblity can also trigger heavy rubs.
-Operation load: Sufficient exact and comprehensive knowledge is crucial for the evaluation of the failure progression and the risk. Thereby, in case of a predeterioration, the design data may not be sufficient. This is the case, if the part now got sensitive also for other influences. For example an acceleration of the cyclic crack propagation through creep and corrosion can affect safety relevant, different to the new part, the time lapse.
Also effects like the change of the load during the failure progression must be considered. That is also true e.g., for the diminishing remaining cross section, stress rearrangement and heat balance. This reacts at a changed cooling flow or a, by a crack deteriorated, heat dissipation.
Fig. "Numbers of sensors for online monitoring" (Lit. 25.2.1-9, Lit. 25.2.1-11, 25.2.113, 25.2.1-14, 25.2.1-17, 25.2.1-19, 25.2.1-20): In the following a survey of
sensors/probes for the continuous (on-line) aeroengine monitoring
should be given (succession no evaluation of the importance):
„1“ Vibration sensors (Fig. "Engine health monitoring with data fusion", Fig. "Condition indicator using vibration sensors" up to Bild 25.2.1-9): These `pickups' (for acceleration, vibrations; high frequency vibration sensors = HFVS) measure accelerations on vibrating surfaces. Thereby several problems arise: The position of the pickup must fit as optimal as possible to the problem to be monitored (Ill. 25.2.1-5). Usually one resides on the gear casing and one per front and rear flange. Not always the positions are optimal. For example bearing failures can be identified best with sensors on the static outer ring and not on the supporting outer casing. This is expecially true for dampened elastic suspended bearings (Fig. "Oil dampened roller bearing vibration"). In the most unsuitable case, acceleration amplitudes already below the before adjusted threshold, can trigger dangerous failures. An example are fractures of turbine rotor blades in the high pressure area of three shaft aeroengines. The thresholds can not be selected arbitrary low, because otherwise the probability of alarm messages gets too high (Fig. "Data Fusion and information fusion"). High acceleretions and high temperatures (in the hot parts region) load the sensors itself. This can confuse with dropout and indication errors.
For the completeness should pointed here pointed at special techniques for the monitoring of blade vibrations during test runs. Primarily concerned are at the blades applied strain gauges (volume 3, Ill. 184.108.40.206-3 and Ill. 220.127.116.11-4). Also an electric conductor in the casing and a little magnet in the tip of the rotor blade (compressor, because of the temperature) can be used for vibration measurements (volume 3, Ill. 18.104.22.168-3).
„2“ Fire sensors (Fig. "Magnetic chip detectors potential problems" and volume 2, Ill. 9.5-2) register unacceptable high temperatures in the surrounding. These are mostly mounted at the wall of an aeroengine nacelle. From experience these suffer especially under malfunctions of plugs and cable connectors.
„3” Temperature sensors monitor many components and systems. In the hotgas stream they have, besides mechanical overloads, also problems with changes during long periods (oxidation, erosion, changes of material structure, changes of insulation). These can cause the drift of the data (Ill. 19.2.1-7).
„4” Pressure sensors serve the compilation of data in the main stream for the control unit of the aeroengine (Fig. "Health monitoring structure"). Additionally these are also needed for a trend monitoring/health monitoring.
Above this, these are an important function monitoring of the systems from oil and fuel and supply data for the aeroengine control unit. The application of especially fast responding sensors shall also help to prevent compressor surge (volume 3, Ill. 22.214.171.124-3). Because the flow velocity acts at the pressure sensors, these underlie influences like contamination/ blocking and icing. This can have dangerous consequences for the aeroengine control unit (volume 1, Ill. 4.2-3).
„5“, „7” Flow velocity/measuring of the flow rate: These measurements are espesially needed for the control of the fuel supply and the monitoring of the oil flow rate. Changes of the incident flow at the sonde (icing) or temperature changes in the medium influence the measurement data. This applies e.g., for the air stream at the compressor intake (volume 3, Ill. 126.96.36.199-14 up to Ill. 188.8.131.52-16).
„6“ Rotation speed sensors are preferably used for main shafts. In the compressor characteristic diagram (operating map), we find so called speed characteristics, to which important operation data are assigned (volume 3, Ill. 184.108.40.206-7). Maximum determined rotation speeds must not exceeded. However, for fractures of shafts, sensores are often overcharged in its response time. Therefore additionally facilities are used, which shall prevent an overspeed (volume 1, Ill. 4.5-8 and Ill. 4.5-9).
Changes of the acceleration behavior respectively rotation speed, changes can point at developing or already occurred failures. To these belong rubbing events or the influencing of the gas flow (e.g. failures of the blading).
Magnetic chip detectors (Fig. "Magnetic chip detectors potential problems", QDM-sensor Fig. "Monitoring particle formation in oil" and Fig. "Time limits of chip detector warning") differ from simple `magnetic plugs'. They are in the position to monitor the oil flow for magnetic particles. The particles must be separated without unacceptable influencing the oil flow. For this it must be suitable deflected. The detectors need a periodical maintenance. Thereby the particle agglomerations must be removed to activate the display function new.
„9” Position sensors serve the verification and feed back to the actuating system. In the most simple case end switches are concerned. To actuating systems belong variable nozzle guide vanes of the compressor, thrust nozzles, thrust reverser and the fuel control unit.
Sufficient fail-safe sensorsn are a requirement for the measurements of tip gaps from rotor blades of compressors. This would be needed for the adjustment of optimal tip gaps during operation. However such a facility did not yet arise for serial use, at least till now.
„10“ Particlwe detection in the stream of the intake and the exhaust (Bild 25.2.1-3):
Such sensors use the electric charge of the particle transporting stream (Fig. "Foreign object detector in the gas stream"). These register size, amount and velocity, as well as up to a certain degree, also the chemical composition of the transported particles.
A so called 'inlet debris monitoring sensor' (IDMS) is positioned in front of the fan in the intake stream.
An `engine distress monitoring sensor' (EDMS) monitors the exhaust gas stream. For this there are at least test rigs. These operate in the stream with sensors of electric charged structures. With these, unusual rubbing processes and erosion processes can be recorded/identified at the abrasion and other OOD-particles (from the engine itself =own object damages).
„11” Noise recordings with the `cockpit voice recorder' (CVR) will be analyzed in special cases for hints at a failure sequence (volume 1, Ill. 4.2-4 and volume 1, Ill. 4.2-5). Thereby for example valuable findings can be gained from noises of the fan or from gears .
Several, on the „sound path“ (flanges and gear casings) suitable positioned so called `stress wave analysis sensors' (SWAN, Lit. 25.2.1-.9), measure the energy of the sound waves in the ultrasonic region. These work on the basis of piezo transducers and let identivy also shocks and rubbing processes.
„12” Continuous oil analysis get possible with new developments ('oil condition monitor' =OCM) which are in the test phase. These devices are in the position to monitor the oil condition on-line. The device shows contaminations from aging products, water and fuel. Additionally the concentration of the additives is identified.
Fig. "Foreign object detector in the gas stream" (Lit. 25.2.1-9 and Lit. 25.2.1-18): The electric charge of a flow is influenced from
transported particles. Thereby velocity, material and size of the particles play a role. This allows to conclude
from the charge measurement at the particles.
The structure of a particle monitoring system shows the sketch above. Especially the signal processing seems complicated.
Below, a measurement plot from the test run is displayed. It shows the change of the charge above the time, respectively the rotation speed. A rubbing of rotor blades tips in the compressor (Fig. "Failure identification by gas path analysis") at high rotor speeds shows a large amplitude.
For forecasts and to prevent false alarms, a combination of measurement data of other monitoring systems (Fig. "Engine health management") seems suitable.
Fig. "Failure identification by gas path analysis" (Lit. 25.2.1-7 and Lit. 25.2.1-8): This picture shows three examples at a small fan
aeroengine which have been identified with help of the
„gas path analysis“ (sketch middle).
Example 1 (upper diagram): Identification of a rubbing process at the blade tips of the high pressure turbine (gaser producer).
Starting point was the rise from the gas temperature behind the gas producer (LPT-entrance temperature), with a drop of the rotation speed (speed of the high pressure, system). Thes assessable trends demanded no exceeding of usual temperatures or rotation speeds. With this the risk of unusual loads during the test run is avoided. Symptoms of a failure occurred neither during operation nor at a ground run.
The problem was so early recognized, that at the high pressure turbine only the exchange of a seal segment (turbine shroud) was necessary.
Example 2 (diagram middle): In this case a blocked fuel nozzles were concerned. This caused a nonuniform flame (flame streaking). Aso here the gas temperature behind the gas generator rose with dropping rotation speed. The recognition of the trend in time enabled the exchange of the aeroengine before a catastrophic failure. Probably this would have been occurred during longer locally overheaqting of the combustion chamber and the turbine (volume 3, Ill. 220.127.116.11-1 and Ill. 18.104.22.168-3).
Example 3 (diagram below): Rubbing of the gas producer compressor (high pressure compressor). The process takes place over a longer time period. This show the relativly slightly pronounced trends. Thereby the fuel consumption increased with the gas temperature. This is typical for a lasting efficiency drop (deterioration). At the same time, the high pressure rotation speed decreased slightly. After a for the operation behaviour critical condition was reached (e.g., too high gas temperature, compressor surge), the aeroenging could be changed without logistics problems.
Fig. "Condition indicator using vibration sensors" (Lit. 25.2.1-1): Used are
vibration sensors (acceleration pick
ups) for the direct measure of mechanical oscillations (e.g., of walls and flanges) and indirect vibrations of
gas fluctuations. These can also be measured by pressure sensors (e.g.,
Kulite®). To the standard equipment belong
three sensor positions: High pressure compressor, low pressure turbine and accessory gear. The analysis
is electronic. For this, signals of different sensores are combined. So, location and components of
the vibration cause can be determined, with low risk of an indication error.
Within the aeroengines, sensors/probes are used for the detection and analysis of different deteriorating vibrations. Concerned are e.g., consequuences, respectively symptoms of foreign object entry, compressor surge or failures.
Typical positions are shown for the aeroengine of a fighter. These serve the monitoring of:
Fig. "Elements of a vibration monitoring" (Lit. 25.2.1-6 and Lit. 25.2.1-17): Vibrations of shafts and main bearings can be monitored by the deflection. The signals of the sensors are analyzed in different ways:
Sensors for accelerations (seismic velocity transducers, accelerometers, vibration meters, spectrum analysers, frame right). With the spikes in the measuring data diagrams, the concerned/deteriorated component can be identified at its typical vibration frequency. Requirement are extensive vibration calculations/analysis which usually are carried out already during the design phase.
Fig. "Oil dampened roller bearing vibration" (Lit. 25.2.1-10): Oil dampened bearings
(roller bearings, Fig. "Damped main bearings") can suppress
shaft vibrations. This desired property however hinders the vibration monitoring for the identification
of problems. With this, the danger exists, that dangerous vibratios in the shaft system don't get to
the sensors at the outside (e.g., casings). So turbine rotor blades
of a three shaft engine with blade
fractures have not been identified by the acceleration
A detection of unusual vibrations is only then possible, if with the failure also the damping effect fails. This is the case when it comes to the direct contact of the components:
However at least the function of the bearing
damping can be monitored. This can underlie
seveal influences (framed upper sketch).
The diagram below compares the clculated behavior with the measured. Thereby influences at the damping oil film, and with this at the casing, vibrations play a role. It comes during the acceleration and deceleration of the rotor to larger amplitudes of the deflection. Thereby the spring effect in the oil film stiffens (non newtonian behaviour). This can falsify vibration measurements. However, like it can be seen in the comparison with the measurement data (continuous line), it can be mathematical well modeled (broken line).
Fig. "Assessment of vibration measurement" (Lit. 25.2.1-10): The frame above shows schematically the vibrations monitoring of an aeroengine. With this, the following problems should be controlled.
A special challenge is the detection of gear faults/failures with the help of vibrations of the casing. These can be triggered by failures of gear shafts (chapter 23.2.1):
Different than at other gear failures, primarily to identify with trend analysis of the vibration energy or at signal forms (diagramm below). Requirement for a success is the use of known parameters from component specific failure trends. Thereby also a synchronisation of the sensor impulses with the rotation speed can be helpful.
Fig. "Shaft problem analysis assessing vibration" (Lit. 25.2.1-10): Not aligned shafts
induce unbalances. With this the module
design and the exchange of accessory
devices will be a challenge. Two typical situations can be distinguished
A shaft which rotates in bowed a condition aroung a straight axis (left).
Rotation around a bowed axis/centerline (right) corresponding a flexible shaft (volume 3, Ill. 22.214.171.124-13). To both conditions, frequency distributions of the amplitude peaks can be assigned (diagrams below).
Ill. 25.1-9.2 (Lit. 5.1-9): For a long time it is tried
to identify contact-free, cracks in the stable propagation phase in rotating
Firstly the approach of vibration measurements at the bearing outer rings and/of the casings was pursued. Thereby unusual vibrations, caused by little unbalances should serve. Rather promising seems the change of the Torsion vibrations from a shaft by crack formation in the blading. Here the effect is used, that such cracks (thermal fatigue, blade vibration, creep) run preferential in axial direction. The closer the crack is positioned at the blade root, the more it influences its bending vibration. This effects markedly the frequency of the torsion vibration from the shaft during operation.
The proof of the function was provided by the OEM in test rig experiments.
For this, at a suitable place of the shaft circumference a periodical reflexion face (here 60 `teeth') was placed. This is illuminated with a glass fiber bundle, which transferres the reflexion-light pulses to a processing unit (sketch above). Three blades of a high pressure turbine disk have been suitable prepared. During two rotation speeds, the lapses of the torsion frequencies have been measured and analyzed (diagram below). From the characteristic amplitude peaks and associated frequencies the blades could be identified with a frequency shift. When this method, as far as the development is successful gets into aeroengine service can not be foreseen at this time.
Fig. "Pyrometer for monitoring turbine rotor blades" (Lit. 25.2.1-3, Lit. 25.2.1-4 and Lit. 25.2.1-19):
Pyrometers can directly monitor the temperature of the
blades of a turbine rotor stage. With this, a requirement for the identification of
the lifetime consumption is given. This is of high importance for the
prevention of failures and the
A pyrometer (sketch above) consists of a lens system that hints directly at a specified blade area. At modern installations, the light is transferred to a reciever (photo cell, Fig. "Pyrometer"). The necessary flexible light cable consist from many single fibres. It makes it possible to mount the electronic in the colder region, outside at the aeroengine.
A pyrometer has spezific problems (more detailed description in Fig. "Pyrometer"):
Here should be also mentioned the possibility of a so called pulse pyrometer (frame below). These sensors are already used in industrial gas turbines and at test rigs. Such pyrometers use the stroboscopic effect, to determine the temperature respectively its distribution at individual rotor blades. With this the possibility exists, to identify and exchange single blades with increased material temperaure. Such an individual temperature increase can be caused from a disturbance of the cooling air guidance. For this, blocking/clogging (volume 3, Ill. 126.96.36.199-2) or foreign object impacts (carbon impact, volume 1, Ill. 188.8.131.52-12 and volume 3, Ill. 184.108.40.206-6.1) are typical.
Fig. "Individual blades temperature monitoring" (Lit. 25.2.1-2 and Lit 25.2.1-25): This is an example of a facility in industrial
application for the measuring of the individual surface temperature of
turbine rotor blades (diagram below). This measurement can occur at up to 30 points per blade. So temperature profiles can be generated.
The sketch above shows the scheme of the installation. A control unit uses the signals of a rotation phase recording for a `stroboscopical' optical pyrometer. So individual rotating blades can be selected for the measurement.
The temperature data are passed through a data processing to the data analysis. The results can be digital stored. They cam be adjusted for frequent questions with displays at the screen. In critical cases, an automatic alarm is triggered.
Advantage of this analysis are:
This can also be helpful for the logistics, respectively the specification of
overhaul intervals or
The individual blade monitoring is in the position to minimize effort and costs, as only concerned parts are exchanged or treated.
Fig. "Sensor in oil stream ODM for metallic particles" (Lit. 25.2.1-21 and Lit. 25.2.1-22): There is development since the beginning 90s at
in-line oil debris monitors (ODMs). In contrast to the magnetic chip detectors (magnetic debris
monitors = MDMs., Fig. "Monitoring particle formation in oil"), they can also react at
unmagnetic metallic particles. These sensors are
for aeroengines of the newest fighter generation in the series introduction. They enable a
continuous electronic analyzable monitoring of the whole oil
stream, without influencing it unacceptable,
for example with a high flow resistance.
ODMs use instead of a constant magnetic field a high frequency alternating current, to attract ferromagnetic particles (sketch above). This excites two field coils in different direction, with corresponding poled magnetic fields (middle sketch). A `measurement coil' (sensor) reacts at changes of the field, caused from the particles, which are transported from the total oil stream into a tube, concentric to the coils. So the whole number of particles above a adjustable trigger threshold, can be continuously counted and observed. With this it is possible, to suggest at the size and type of the particle by means of the phase and amplitude (diagram below).
The amplitude of the signal is for magnetic particles proportional the mass. For unmagnetic Particles it reacts at the size of the surface, however with `reverse' phase. Several trigger thresholds enable a classification of the particles in size classes (Fig. "Chances by inductive ODM technology").
Fig. "Chances by inductive ODM technology" (Lit. 25.2.1-21 and Lit. 25.2./-22): The chart above shows the typical
trend of a race deterioration by fatigue, from an anti friction bearing. It occurs at race tracks
of bearings (Fig. "Fatigue pittings at bearings") and tooth flanks of gears (Fig. "Development of fatigue puittings").
A typical time depending deterioration behavior, that can be related three fields, can be observed.
The described failure behavior during fatigue is well reprocuced by the ODM measurements (diagram below). The smaller the particles, the more pronounced it gets. The trend of the curve is naturally influenced, as consequence of the failure, by load changes like vibrations, particles and static loads. With this it can also concluded at risks during further operation (Fig. "Example for monitoring with ODM").
Fig. "Example for monitoring with ODM" (Lit. 25.2.1-21 and Lit. 25.2.1-22): The diagram shows a failure of an anti friction bearing from a modern fighter engine during the run on a test rig.
Fig. "Benefits by unloading of a rolling bearing" (Lit. 25.2.1-21 and Lit. 25.2.1-22): The
speed of deterioration rises with the
load, which show the curves of the particle access markedly. This enables comparing
conclusions at the rolling surfaces, respectively load on the
part. So it is thinkable, to conclude
at hight and point of time of deteriorating loads. Thereby e.g.,
dynamic loads from unbalances or static loads from axial
bearing thrusts, caused by larger labyrinth gaps, are concerned (volume 2, Ill. 7.2.1-2 and Ill. 7.2.1-3).
Such findings enable measures like a reduction of the load
as certain maneuvers till the exchange of the concerned main bearing can be ruled out. At fighters this would be a interdiction of high speed flights near the ground.
In the shown case obviously the bearing load could be reduced. This markedly shows the curve trend of the particle access.
25.2.1-1 T.Brotherton, P.Grabill, R.Friend, B.Solomayer, J.Berry, „A Testbed for Data Fusion
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25.2.1-4 „Measuring HPTB surface temperatures”, Zeitschrift „Power Plant Technology Economics & Maintenance“, January/February 1997, Page 30-32.
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25.2.1-8 „About Gas Path Analysis (GPA), Case Studies 1-6”, www.jet-care.com, Page 1 -8.
25.2.1-9 A.J.Volponi, T.Brotherton, R.Luppold, D.L.Simon, „Development of an Information Fusion System for Engine Diagnostics and Health Management“, Paper NASA/TM-2004-212924 der „39th Combustion/27th Airbreathing Propulsion/21st Propulsion System Hazards/ 3rd Modeling and Simulation Joint Subcommittee Meeting”, Colorado Springs, Colorado, December 1-5, 2003, Page 1-17.
25.2.1-10 G.J.Ives, P.Jenkins, „A Joint Study on the Computerisation of In-Field Aero Engine Vibration Diagnostics“, Proceedings AGARD-CP-448 Quebec, 30 May - 3 June 1988, Page 31-1 up to 31-13.
25.2.1-11 „Temperature Sensors”, Fa. Weston Aerospace, www.westonaero.com, Page 1 -4.
25.2.1-12 Airworthiness Directive No. 96-ANE-35-AD, Amendment 39-14339, AD 2005-21-01, „Pratt & Whitney JT8D-200 Series Turbofan Engines“, Page 1 -8.
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25.2.1-15 Reference 05-105/MSG-211, „'Engine Systems”, Page 192-201.
25.2.1-16 Technical Information Nr. 1110-PD-001-0-00, „Identifying and Correcting Temperature Control Problems“, Fa. Barber-Colman Co., Page 8-2 up to 8-12.
25.2.1-17 C.Fisher, N.C.Baines, „Multi-Sensor Condition Monitoring Systems for Gas Turbines”, Paper H2 der „International Conference on Condition Monitoring“, Brighton, England: 21-23 May, 1986, Page 295-305.
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25.2.1-19 K.Bauerfeind, „Steuerung und Regelung der Turbotriebwerke“, Birkhäuser Verlag, 1999, ISBN 3-7643-6021-6, Page 141-156.
25.2.1-20 AFRL, Paper Pr-00-03, „Sensor Technology Improves Jet Engine Reliability”, www.afrlhorizons.com, Page 1-3.
25.2.1-21 „In-line oil debris monitor, a System which detects debris in oil prevents catastrophic engine failures“, Zeitschrift `Aerospace Engineering,' October 1996, Page 9 up to 12.
25.2.1-22 K.Cassidy, „Qualifying an On-Line Diagnostic and Prognostic Sensor for Fixed and Rotary Wing Bearings and Gears”, Proceeding der IEEE Aerospace Conference, Big Sky, MT - March 2008, Page 1-25.
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25.2.1-24 Land Instruments International, „Combustion Turbine Blade Temperature Analysis”, www.landinst.com, 21.Sept. 2006.
25.2.1-25 A.Rossmann, „Industrie Gasturbinen. was der Betreiber wissen sollte“, ISBN 3-00-008428-2, erweiterte Auflage 2009, Chapter 3.3.1.