"Development of experimentally-validated models of gearbox lubrication systems for the health-monitoring of aircraft engines"

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Universit`

a di Pisa

Scuola di Ingegneria

Dipartimento di Ingegneria Civile e Industriale MASTER DEGREE THESIS

IN

AEROSPACE ENGINEERING

Development of

experimentally-validated models of

gearbox lubrication systems for the

health-monitoring of aircraft engines

Supervisor:

Prof. Gianpietro Di Rito Prof. Ing. Luca d’Agostino

Author: Andrea Marrai

17 july 2018

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”Run! Rabbit, run! Dig that hole, forget the sun and when at last the work is done, don’t sit down it’s time to dig another one..”

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Abstract

This master thesis focuses on the development of a mathematical model, in order to monitor the evolution of the physical quantities envolved in a gearbox lubrication system of a military aircraft and evaluate possible failures through a Physics of Failure (PoF) based prognostics method.

Experimental data have been acquired during tests in Avio Aero s.r.l. and subse-quently a characterisation of the gearbox lubrication system behaviour has been carried out with a Matlab-Simulink model. A preliminary system identification of the principal system parameters have been necessary due to the lack of informa-tions regarding the system.

The goal of the model developed is not only to predict the behaviour of the physical quantities during tests, but also to simulate different functioning conditions from the nominal one, which may be representive of a system failure. In addition to this, a particular attention has been paid on mantaining the model as simple as possible in order to allow real time calculations. The results obtained has been validated through a comparison between them and the experimental data acquired during tests.

Finally the model have been tested introducing in it different values of a system parameter in order to analyze the main differences between the nominal system and the ”damaged” one. These prognostic models have been used to locate a trend of the physical quantities when a parameter changes in order to obtain an estima-tion of the remaining useful life of the system and the progression of components degradation.

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Lista dei Simboli

µ Absolute viscosity

ηpto Bouc Wen Model Parameter n.1

ν Cinematic viscosity

˙

Wcooler Cooler heat rate absorption

Dcool Cooler orifice diameter

mcooler Cooler thermal mass

ρ Fluid density

f Frequency

Dgbx Gearbox orifice diameter

mgbx Gearbox thermal mass

Cp Heat transfer coefficient

Qingbx Oil Flow at the gearbox inlet

Qcooler Oil Flow in the cooler

Pic Pressure at the cooler inlet

Poc Pressure at the cooler outlet

Pig Pressure at the gearbox inlet

Pog Pressure at the gearbox outlet

∆Pcooler Pressure drop across the cooler

∆Pgearbox Pressure drop across the gearbox

∆Pdelivery Pressure rise across the pump delivery stage

∆Pscavenge Pressure rise across the pump scavenge stage

ωpto PTO shaft angular speed

Jpto PTO shaft moment of inertia

Ddel Pump delivery stage displacement

Qleak Pump leakage

Dscav Pump scavenge stage displacement

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Tt Tank temperature

mt Tank thermal mass

Tic Temperature at the cooler inlet

Toc Temperature at the cooler outlet

Tig Temperature at the gearbox inlet

Tog Temperature at the gearbox outlet

τpump Transmission ratio bettween PTo shaft and

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List of Figures

1.1 Hierarchy of prognostic approaches [1]. . . 4

1.2 Position of recorded parameter TT2, PT2, PS3 and T5. . . 6

1.3 Wind Turbines. . . 8

1.4 Alarm limits and measured data at pressure side. . . 10

1.5 Architecture of the algorithm. . . 11

2.1 Example of an accessory gearbox and its components for civil avia-tion applicaavia-tion [2]. . . 14

2.2 Mechanical arrangement of accessory drives [3]. . . 15

2.3 Mechanical arrangement of internal gearboxes [3]. . . 16

2.4 A typical lubrication system for an engine with 3 bearing compart-ments [2]. . . 20

2.5 Cutaway of a typical double stage oil pump. . . 23

2.6 A Low-Pressure fuel-cooled oil cooler [3]. . . 24

2.7 Gearbox oil system reduced. . . 26

2.8 ωpto complete experimental data. . . 28

2.9 System pressure drops complete experimental data. . . 29

2.10 Pump pressure rise complete experimental data. . . 29

2.11 Temperatures complete experimental data. . . 30

2.12 ωpto useful experimental data. . . 31

2.13 System pressure drops useful experimental data. . . 31

2.14 Pump pressure rise useful experimental data. . . 32

2.15 Temperatures useful experimental data. . . 32

2.16 Constant approximation for the pressures Pt and Pog . . . 34

2.17 Gearbox oil system reduced. . . 34

2.18 Pump modeling and oil massflow circuit representation. . . 37

2.19 Input Mpto related to ωpto/ωptomax. . . 39

2.20 Generation of the input Mpto for the simulation. . . 40

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LIST OF FIGURES

2.22 Shaft dynamics Simulink block diagram. . . 41

2.23 Pressure dynamics and oil Simulink block diagram. . . 42

2.24 Temperatures dynamics block diagram. . . 43

2.25 Tig Simulink block diagram. . . 43

2.26 Tic Simulink block diagram. . . 44

2.27 Dissipations in the mechanical transmission. . . 45

2.28 Toc Simulink block diagram. . . 45

3.1 PTO shaft angular speed and its residue. . . 48

3.2 Input PTO Torque. . . 49

3.3 Comparison between ∆Pdelivery from system response and Experi-mental Data and its residue. . . 49

3.4 Comparison between ∆Pscav from system response and Experimen-tal Data and its residue. . . 50

3.5 Comparison between ∆Pgbxfrom system response and Experimental Data and its residue. . . 51

3.6 Comparison between ∆Pcooler from system response and Experimen-tal Data and its residue. . . 51

3.7 Comparison between Tic from system response and Experimental Data . . . 52

3.8 Comparison between Toc from system response and Experimental Data. . . 52

3.9 Comparison between temperatures from system response and Ex-perimental Data. . . 53

4.1 Residue between simulated failure and nominal system. . . 55

4.2 Trend of the residues peak values when µ changes. . . 55

A.1 GT-SUITE Model. . . 65

A.2 GT-SUITE system response for the pump angular speed. . . 65

A.3 Different Loss mode in the GT-Suite OrificeConn. . . 66

A.4 Pressure rise of the delivery stage of the pump. . . 67

A.5 Pressure rise of the scavenge stage of the pump. . . 67

A.6 GT-Suite Home page. . . 68

A.7 GT-Suite Home page. . . 69

A.8 GT-Suite Case Setup Dialogue Window. . . 70

A.9 Dialogue Window oF the Pump component . . . 71

A.10 Dialogue Window showing calculations in progress. . . 72

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LIST OF FIGURES A.1 ωpto and ∆pscavenge comparison between system response and

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List of Tables

1.1 F124 Engine Parameters at Max. Regime . . . 6

2.1 Simulation configuration parameters. . . 38

2.2 Initial values of the sperimental data . . . 39

2.3 Thermodynamic quantities value. . . 40

2.4 Input Values . . . 40

3.1 Reference values of oil flow rate and pump angular speed . . . 46

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Lista degli Acronimi

AGB Accessory Gearbox

ANN Artificial Neural Network

APU Auxiliary Power Unit

BEC Back up Electronic Control unit

BHMIES Blade Health Monitoring and Integrity Evalu-ation System

CGV Compressor Guide Vanes

ECU Engine Control Unit

EH Engine Hours

FADEC Full Authority Digital Engine Control

FAST Fatigue, Aerodynamics,Structures and Turbu-lence

GTE Gas Turbine Engine

IDG Integrated Drive Generator

MATLAB Matrix Laboratory

PHM Prognostic and Health Monitoring

PMA Permanent Magnet Alternator

PoF Physics of Failure

PTO Power take-off

Rul Remaining Useful Life

WT Wind Turbine

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Introduction

During the Internship at Avio Aero, in Brindisi, the author had the chance to assist at several engine tests in the test cells scenario as a Test Engineer. In this context had been possible to understand the needs of the aircraft engines world, which is in constantly growth and the requirements that a leading company in the aeronautic field must have in order to satisfy them.

During this time had been analyzed the experimental data acquired from the Acceptance Test of a military aircraft auxiliary gearbox in order to manage possible failures during the tests and to resolve them.

Due to the strong interaction between the system and the test rig, the study of the main system components functioning had been advantageous. Amongst all the failures observed during the overhaul of the gearbox, the ones concerning the lubrication system were the more recurring. For this reason had been decided to focus on them.

Prognostic and Health Monitoring (PHM) is an important and growing focus in the design and maintenace of complex systems, indeed, prognostics predicts the future performance of a component by assessing the extent of deviation or degra-dation of a system from its expected normal operating conditions. This lack of performance is most often a failure beyond which the system can no longer be used to meet desired performance. The predicted time then becomes the Remaining Useful Life (RUL), which is an important concept in decision making for contin-gency mitigation.

In Chapter 1 different applications of PHM in the aerospace scenario have been introduced, by presenting different approaches and instruments used. In Chapter 2 the main components of a gearbox lubrication system and its basic requirements have been introduced. In the same Chapter, the lube system hydraulic scheme has been illustrated, by explaining its functioning and the testing activitites conducted. Furthermore, the experimental data acquired during tests have been presented and the extrapolation of the useful data for the aim of the simulation have been ob-tained. The model equations needed assumptions in order to implement the model

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INTRODUZIONE on the SIMULINK software. Model parameters and initial conditions have been introduced as well as the SIMULINK block diagrams representing the system of equations. In Chapter 3 the simulation results are shown by comparing the sys-tem results with the experimental data and giving a representation of the physical quantities residues.

In the final Chapter the model has been tested when changing a parameter in order to evaluate a trend representing a starting point for a comparison meter between a ”Healthy” system and a ”damaged” one. This permits to achieve a prediction of the system health and its remaining useful life.

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Chapter 1 Virtual-Testing and

Health-Monitoring of Aircraft

Systems

Air traffic is continuously growing, and airplanes need to mantain high levels of safety and be more efficient, in terms of both costs of production and sustainable development.

Overhaul and servicing are a big part of the expenses that the companies have to face, after the purchase of the airplane itself. Not only engineers and technicians have to be paid, replacement parts have to be bought, but the airplanes can remain grounded for quite a long period while being repaired. Flights can also be delayed or cancelled, leading to a loss of time and money for the companies.

Maintenance and overhaul play a foundamental role in the life of an engine. Nowadays engine manufacturers do not wait for a failure to occur, they monitor the system parameters during its life and operate servicing when needed to antic-ipate potential failures. This approach, known as Prognostic Health-Monitoring (PHM), brings to a benefit from an economic point of view for engine’s manufac-turers since the overhaul would be their responsibility; it is indeed less expensive to correct the defaults before malfunctions occur than to wait for bigger and more expensive component to break. The downtime can also be reduced.

The PHM approach allows the companies to obtain more reliable systems and to benefit from a better reputation which can help to sign new contracts and thrive on the market.

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CHAPTER 1. VIRTUAL-TESTING AND HEALTH-MONITORING OF AIRCRAFT SYSTEMS

A key point about prognostics approaches classification is building a way to obtain a standard methodology for prognostics applications development within a standard framework. In general, prognostics approaches can be classified into four types:

• Reliability based approach; • Physics-based approach; • Data-driven approach; • Hybrid approach.

The complexity, cost, and accuracy of prognostics techniques is inversely propor-tional to its applicability (Fig. 1.1). Increasing prognostics algorithm accuracy with low cost and complexity is a big challenge.

Figure 1.1: Hierarchy of prognostic approaches [1].

Below a few sections which illustrate different examples of Health monitoring approaches in the aerospace scenario are presented. The instruments and methods used by the different authors of each examples have been taken into consideration to evaluate how to best achieve the objective of this thesis.

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1.1 The Engine F124-GA-100

Engine monitoring systems were introduced to the gas turbine engines in late 70’s and early 80’s to both military [4] and civilian [5] operated Gas Turbine Engines (GTE). Continuously with their development the amount of information provided by these systems was growing and it was implemented into the engine operation and maintenance procedures that were transforming from usage based to condi-tion based philosophy. This was happening in much smaller extent in countries of the Eastern Block, where the usage of based maintenance without extensive use of monitoring systems was common practise till the end of twentieth century. This was true above all for military operators. Sometimes it happened, that even after acquisition of modern engines with implemented monitoring systems, data from these systems are more or less just downloaded and stored. Their usage for the operation and maintenance planning is very limited. This was the case of the Czech Air Force operated F-124 engine powering the L-159 ALCA jet trainer. Gas turbine engine monitoring can be divided into two parts – health monitoring and usage monitoring. Health monitoring is based on analysis of engine operating pa-rameters – gas path pressures and temperatures, vibrations, oil contamination, etc. Usage monitoring is analysing operating time and cycles of the engine in order to estimate its remaining life.

Honeywell F124-GA-100 is a low-bypass two spool engine, with three stage tita-nium blades fan and five stage mixed compressor (four axial stages and one radial stage). The burning of fuel takes place in an annular combustor. Fan and high pressure compressor are powered by single stage high pressure turbine followed by a single stage low pressure turbine, respectively. Both turbines are followed by mixing chamber for first and second stream. Finally the mixed gas is discharged by a fixed nozzle section. The engine main parameters are presented in Table (1.1) [6].

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Thrust F

Bypass ratio BPR

Hight pressure spool speed NH Low pressure spool speed NL Burner exit temperature T4 Turbine exit temperature T5

Overall pressure ratio OPR

Air mass flow rate W

Table 1.1: F124 Engine Parameters at Max. Regime

The engine is controlled by full authority digital engine control (FADEC). FADEC is composed of electronic control unit (ECU) and back up electronic con-trol unit (BEC). ECU is the main engine concon-troller. Depending on the required thrust from the engine control lever the ECU adjusts the fuel flow rate. It also controls setting of the anti-surge devices - the compressor guide vanes (CGV) on the first stage of the high pressure compressor and the compressor bleed bend. ECU unit is placed apart the engine in the airframe behind cockpit. BEC unit is located at the bottom of the compressor casing and provides selected backup data on the state of engine for ECU in case of loss of primary source data. Secondary BEC´s function is a full engine management in the event of ECU failure.

Performance trending data are used to track changes in engine performance during its operation. According the engine documentation performance trending data is recorded at takeoff regime. But it does not specify other conditions for logging the snap shot data.

Figure 1.2: Position of recorded parameter TT2, PT2, PS3 and T5.

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CHAPTER 1. VIRTUAL-TESTING AND HEALTH-MONITORING OF AIRCRAFT SYSTEMS TT2 and T5. All of them is part of performance trending data are shown. The performance data consist of these parameters:

• Engine Hours (EH) [Hour].

• Inlet total temperature (TT2) [degF]. • Exhaust gas temperature (T5) [degF]. • Inlet total pressure (PT2) [psi].

• Compressor discharge static pressure (PS3) [psi]. • Compressor spool speed (NH) [rpm].

• Fan speed (NL) [rpm].

• Compressor guide vane position (CGV) [deg.]. • Commanded engine fuel flow (WFM) [dg.s-1].

From the analysis of the performance data it is possible to determine the spe-cific conditions under which the data is being recorded. Pressure PT2 is in the vast majority of cases in range from 95 kPa to 110 kPa and the temperatures TT2 from 270 K to 310 K and both of the parameters are equally distributed around the mean value. Combination of these parameters corresponds with altitudes from ground to 4000 m and the whole range of flight speeds.

Furthermore in the Engine Event Recorder Data are contained various infor-mation during the engine transient health check. The transient health check is automated procedure performed on ground either after engine start or after land-ing. The one health check contains 94 points where the engine thermodynamic parameters are logged together with some extra state and fault codes. The ther-modynamic data might be potentially suitable for engine performance analysis and evaluate, in this way, potential failures or critical values of the measured parame-ters.

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1.2 Health-Monitoring of a Wind Turbine

Figure 1.3: Wind Turbines.

The wind generating power utilisation has proliferated widely in the previous decade in the world and across the India [7]. The installed power industry in India is 22,465 MW up to December 2014, which is a now rank fifth in the world after China, USA, Germany and Spain . As a result, wind turbine industry is being grown up continuously, and becomes more challenging for power engineers to do condition monitoring and health assessment of WTs. In general, every WT is un-der shut-down condition for 0.595– 2.705% time period of a year. This shut-down condition is due to the installation errors, manufacturing defects or effects of age-ing, nasty environmental condition and perturb loading scenario experienced by WT apparatus. Different types of failures occur in the WT generators (WTGs), i.e. failure of components, control system, grid failure due to weak connections, failure due to high wind, lightening, loosening of part and icing, generator, turbine blades, brake system, axle bearing, hydraulic system, pitch mechanism, gear box and yaw system and so on. The imbalance faults in blade, shaft and furl and aerodynamic asymmetry are common imbalance faults in WTGs. The main causes of a blade imbalance are errors in construction or manufacturing, icing condition, degradation due to ageing, or wear and fatigue in the WTG operation. Due to imbalance on blades and rotating shaft, equipments gravitate to shift and wear in varying degree over time. For example, effect of icing condition can develop a blade imbalance due to increasing extra burden by loads on WT supporting tower, which may create fractures and possible to collapse [8] the tower. The aerodynamic asymmetry is due to assorted reasons, containing errors in the control mechanism and high wind shear. For example, due to the error in control system, the pitch angle of any one blade is slightly changed from remaining two. This causes the aerodynamic asymmetry in the WTGs. Furl imbalance faults can be caused by

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CHAPTER 1. VIRTUAL-TESTING AND HEALTH-MONITORING OF AIRCRAFT SYSTEMS changing in initial or fixed rotor/ tail-furl angle in degree which create the im-balance in tail and rotor part of the WT. Hence a small imim-balance can lead to a fault affecting WT, towers and finally WTG’s. Hence an effective monitoring and fault diagnosis of WTG’s can prove instrumental in reducing repair costs, enhance operating life and rule out catastrophic failures. Generally available techniques for imbalance faults identification require additional vibration sensors (i.e. accelerom-eters) and data acquisition system. These vibration sensors are placed on the WT equipment’s surface, which are very difficult to access due to high height of tower during WTGs operation. Furthermore, the components and sensors are naturally subject to failure, and lead extra problems related to stability and reliability of system and extra costs for maintenance. In this paper, the application of simula-tions is investigated to analyse the WTs faults due to imbalance condisimula-tions using ANN technique. The complete WTG models are designed in [9] an integrated do-main of Simulink [10], FAST (fatigue, aerodynamics, structures and turbulence) [11] and TurbSim [12], where TurbSim is used to produce the wind data, com-plete WT dynamics is simulated by FAST, and MATLAB-based Simulink software imitates the dynamics of the electrical generator and related equipments of the WTGs. Simulation observations are then carried out in six distinct conditions, i.e. aerodynamic asymmetry, rotor-furl imbalance, tailfurl imbalance, blade im-balance, nacelle-yaw imbalance and normal operating scenarios for the dynamical model of WTG. Proposed method is applied for imbalance faults identification of WT functioning under capricious speed scenario. and identifies it with higher fault identification accuracy of 100% during training phase and 99.12% during testing phase.

1.3 Blade Health Monitoring and Diagnosis Method

of Wind Turbine

This article [13] proposes the novel diagnosis method for wind turbine blades, which is able to perform real-time blade condition monitoring with high resolution and fault detection. In consideration of the severe internal and external environ-ments of a rotor, real-time condition monitoring for the blades of a wind turbine was realized with optic sensors and a wireless network. A statistical approach is so sensitive in non-stationary states that it cannot be applied to integrity evaluation systems on its own. In contrast, a model-based technique is too insensitive to de-tect faults at the right time. To compensate the flaw of each method, a new hybrid approach method, which merges a statistics-based algorithm with a model-based

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CHAPTER 1. VIRTUAL-TESTING AND HEALTH-MONITORING OF AIRCRAFT SYSTEMS algorithm, is proposed. In addition, in order to improve its reliability, alarm limits are determined through a simple and accurate learning algorithm.

Figure 1.4: Alarm limits and measured data at pressure side.

The proposed method was embedded in the Blade Health Monitoring and In-tegrity Evaluation System (BHMIES) and was tested at a wind turbine WinDS3000 of the Yeongheung wind farm to give a successful demonstration.

1.4 Landing Gear Health Monitoring

Here [14] is an axample of health monitoring applied to an aircraft landing gear. The system develop predicts the time it will take for the brakes to cool to the required take-off temperature and give the pilot a predicted time for pushback. The system works in conjunction with the current Brake Temperature Monitoring System. In Fig.(4.1) is represented the architecture of the algorithm:

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Figure 1.5: Architecture of the algorithm.

The system will give crew and ground staff an estimate of the time when push-back can commence. The following functions will be performed:

• The brake temperatures and aircraft state will be monitored during all on-ground phases from taxi-in and back to runway.

• Predict the amount of energy that will be absorbed into the brake from the given moment up to starting the take-off phase.

• Predict the time for the brakes to cool from the current temperature incor-porating estimated temperature increases on the taxiout phase.

• Estimate taxi-out duration and estimate time to pushback which ensures cool brakes on arrival at runway.

A MATLAB/SIMULINK model of the aircraft state and predicted time for the brakes to cool was constructed to simulate the on ground phases. The brake cooling model was validate with flight test data and the algorithm was tuned using MATLAB code, and then implemented into the SIMULINK model. The brake temperature measurements are subject to substantial noise and require heavy filtering. Good prediction of the eventual cool time can still be achieved ahead of time.

1.5 Physics-based prognostics

Physics of failure (Pof) based prognostics is one of the major methodologies used for prognostics and it is located on the top of the pyramid of prognostics

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ap-CHAPTER 1. VIRTUAL-TESTING AND HEALTH-MONITORING OF AIRCRAFT SYSTEMS proaches as seen in Fig. (1.1). In this approach, a physical model for the system is developed. Thys physical model is a mathematical representation of failure modes and degradation phenomenon. To establish this model, a thorough understand-ing of the system physics is required.In addition to knowledge about the system, knowledge about operating conditions and life cycle loads applied to the system are also required. Modelling of the system can be at a micro or macro level. A macro-level model is based on a first basic knowledge about the system, to model the relation between its components and modelling is performed by mathematical. After establishing the system model, an in situ monitoring of the system is per-formed, then system diagnosis is used to assess its performance. The model can use the knowledge about the current system health and future scenario about the load exposure to forecast the Remaining Useful Life (RUL). Physics-based prognostics has been applied to the systems in which their degradation phenomenon can be mathematically modeled such as in gearbox prognostic module. This methodology is very efficient and descriptive because system degradation modelling depends on laws of nature. It is also accurate and precise, but accuracy and precision depend on model fidelity.

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Chapter 2 Lube System Description and

Model Development

2.1 Accessory Gearbox

Accessory units provide the power for aircraft hydraulic, pneumatic and electri-cal systems in addition to providing various pumps and control systems for efficient engine operation. The high level of dependence upon these units requires an ex-tremely reliable drive system.

The drive for the accessory units is tipically taken from a rotating engine shaft, via an internal gearbox, to an external gearbox which provides a mount for the ac-cessories and distributes the appropriate geared drive to each accessory unit. The Accessory Gearbox (AGB) often includes an Integrated Drive Generator (IDG) which will give the initial motion to the high-pressure shaft at the start-up of the engine. Amongst the accessories, we can find:

• A Permanent Magnet Alternator (PMA); • A starter;

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CHAPTER 2. LUBE SYSTEM DESCRIPTION AND MODEL DEVELOPMENT

Figure 2.1: Example of an accessory gearbox and its components for civil aviation application [2].

The motion is transmitted from the engine to the AGB, through a series of gearboxes. The location of the internal gearbox whithin the core of an engine is dictated by the difficulties of bringing a driveshaft radially outwards and the space available whithin the engine core. Thermal fatigue and a reduction in engine performance, due to the radial driveshaft disturbing the gasflow, create greater problems whithin the turbine area than the compressor area. For any given engine, which incorporates an axial-flow compressor, the turbine area is smaller than that containing the compressor and therefore makes it physically easier to mount the gearbox within the compressor section. Centrifugal compressor engines can have limited available space, so the internal gearbox may be located within a static nose cone or, in the case of a turbo-propeller engine, behind the propeller reduction gear as shown in Fig. (2.2).

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Figure 2.2: Mechanical arrangement of accessory drives [3].

On multi-shaft engines, the choice of which compressor shaft is used to drive the internal gearbox is primarily dependent upon the ease of engine starting. This is achieved by rotating the compressor shaft, usually via an input torque from the AGB. In practice, the high pressure system is invariably rotated in order to generate an airflow through the engine and the high pressure compressor shaft is

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CHAPTER 2. LUBE SYSTEM DESCRIPTION AND MODEL DEVELOPMENT therefore coupled to the internal gearbox.

To minimize unwanted movement between the compressor shaft bevel gear and radial driveshaft bevel gear, caused by axial movement of the compressor shaft, the drive is taken by one of three basic methods shown in Fig. (2.3).

Figure 2.3: Mechanical arrangement of internal gearboxes [3].

Minimum number of components is used when the compressor shaft bevel gear is mounted as close to the compressor shaft location bearing as possible, but a small amount of movement has to be accommodated within the meshing of the bevel gears. Alternatively, the compressor shaft bevel gear may be mounted on a stub shaft which has its own location bearing. The stub shaft is splined onto the compressor shaft which allows axial movement without affecting the bevel gear mesh. A more complex system utilizes an idler gear which meshes with the compressor shaft via straight spur gears, accommodating the axial movement, and drives the radial driveshaft via a bevel gear arrangement. The latter method was widely employed on early engines to overcome gear engagement difficulties at high speed. To spread the load of driving accessory units, some engines take a second drive from the slower rotating low pressure shaft to a second external gearbox. This also has the advantage of locating the accessory units in two groups, thus overcoming the possibility of limited external space on the engine. When this method is used, an attempt is made to group the accessory units specific to the engine onto the high pressure system, since that is the first shaft to rotate, and the aircraft accessory units are driven by the low pressure system.

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CHAPTER 2. LUBE SYSTEM DESCRIPTION AND MODEL DEVELOPMENT The purpose of a radial driveshaft is to transmit the drive from the internal gearbox to an accessory unit or the external gearbox. It also serves to transmit the high torque from the starter to rotate the high pressure system for engine starting purposes. The driveshaft may be direct drive or via an intermediate gearbox .

To minimize the effect of the driveshaft passing through the compressor duct and disrupting the airflow, it is housed within the compressor support structure. On by-pass engines, the driveshaft is either housed in the outlet guide vanes or in a hollow streamlined radial fairing across the low pressure compressor duct. To reduce airflow disruption it is desirable to have the smallest driveshaft diameter as possible. The smaller the diameter, the faster the shaft must rotate to provide the same power. However, this raises the internal stress and gives greater dynamic problems which result in vibration. A long radial driveshaft usually requires a roller bearing situated halfway along its length to give smooth running. This allows a rotational speed of approximately 25,000 r.p.m. to be achieved with a shaft diameter of less than 1.5 inch without encountering serious vibration problems.

The external gearbox contains the drives for the accessories, the drive from the starter and provides a mounting face for each accessory unit. Provision is also made for hand turning the engine, via the gearbox, for maintenance purposes. The overall layout of an external gearbox is dictated by a number of factors. To reduce drag whilst the aircraft is flying it is important to present a low frontal area to the airflow. Therefore the gearbox is ”wrapped” around the engine and may look, from the front, similar to a banana in shape. For maintenance purposes the gearbox is generally located on the underside of the engine to allow ground crew to gain access. However, helicopter installation design usually requires the gearbox to be located on the top of the engine for ease of access. The starter/driven gearshaft roughly divides the external gearbox into two sections. One section provides the drive for the accessories which require low power whilst the other drives the high power accessories. This allows the small and large gears to be grouped together independently and is an efficient method of distributing the drive for the minimum weight. If any accessory unit fails, and is prevented from rotating, it could cause further failure in the external gearbox by shearing the teeth of the gear train. To prevent secondary failure occurring a weak section is machined into the driveshafts, known as a ”shear-neck”, which is designed to fail and thus protect the other drives. This feature is not included for primary engine accessory units, such as the oil pumps, because these units are vital to the running of the engine and any failure would necessitate immediate shutdown of the engine. Since the starter provides the highest torque that the drive system encounters, it is the basis of design. The starter is usually positioned to give the shortest drive line to the engine core.

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CHAPTER 2. LUBE SYSTEM DESCRIPTION AND MODEL DEVELOPMENT This eliminates the necessity of strengthening the entire gear train which would increase the gearbox weight. However, when an auxiliary gearbox is fitted the starter is moved along the gear train to allow the heavily loaded auxiliary gearbox drive to pass through the external gearbox. This requires the spur gears between the starter and starter/driven gearshaft to have a larger face width to carry the load applied by the starter.

2.1.1 Basic Requirements

The AGB is a mechanical piece that gathers a lot of rotating components, which all need lubrication. A whole system is then set to reach well-defined aims. The oil inside of this system has many functions. The main ones can be listed:

• Collect and evacuate the heat produced around the components (such as gears, bearings, joints. . . );

• Redistribute this heat to heat the fuel coming from the tanks;

• Reduce the friction by creating an oil film under the rotating components; • Gather and evacuate the debris created by eventual dysfunction;

2.1.2 Lubrication Circuit

The lubrication systems generally used in commercial auxiliary gearboxes to serve above-mentioned objectives are self-contained recirculatory systems. In such systems the oil is distributed to the locations where it is needed and returned to the tank by pumps. Three subsystems are essential for the circulation of the oil.

• Storage and supply system; • Scavenge system;

• Cooling system.

The function of the storage and supply system is to deliver the required amount of oil to the bearings and gears in a condition that achieves good lubrication. Thus the oil must be filtered and its temperature has to be in the proper range. The system uses the amount of oil stored in the oil tank. The function of the scavenge system is to return the oil from the sumps in the bearing compartments and the gearboxes to the oil tank. In many oil systems the scavenge oil passes a filter before it enters the tank. The cooling system ensures the oil temperature not to exceed required values. The major components of a typical lubrication system are:

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CHAPTER 2. LUBE SYSTEM DESCRIPTION AND MODEL DEVELOPMENT • Tank;

• Pressure pump and supply lines; • Scavenge pumps and return lines; • Filters and strainers;

• Cooler;

• Sensors for flight deck indication and condition monitoring.

The tank fill port and hose connections (for remote filling of the oil tank) are installed for servicing purposes. As each area that needs lubrication has its specific requirement concerning the amount of oil for proper lubrication and cooling, the oil flow to the lubricated areas has to be matched with their demand. This matching is achieved by the cross section of the supply lines and the oil nozzles. Concerning the pressure regulation, two types of systems are in use. The relief valve system, also called the constant pressure system, and the full flow system. In the relief valve system the pressure at the pump exit is maintained at a specific value over the engine operating range by a relief valve that returns excessive oil into the tank. The full flow system operates without any pressure regulation device. Thus the oil flow in the supply lines is a function of the operating speed of the pressure pump, the supply line and oil nozzle cross sections and of the oil viscosity. This leads to a changing oil pressure with changing engine shaft speeds. The pump of a relief valve system also supplies the part of the oil flow that is returned to the tank to keep the pressure constant. It has to be larger and requires more power for operation than the pump of a full flow system. Most systems are designed as full flow systems. This type of system uses smaller pumps compared to the constant pressure system. Such a system saves weight and is easier to adjust, because it has no pressure regulating valve. Independently of the method of supply oil pressure regulation, the subsystems of both system types are practically identical. Fig. (2.4) shows the main components of a typical lubrication system. This example shows a full flow system with a fuel cooled oil cooler. The vent (or breather) system uses a central de-oiler installed on the accessory gearbox.

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Figure 2.4: A typical lubrication system for an engine with 3 bearing compartments [2].

2.1.3 Fluid Properties

Low viscosity synthetic lubricants are tipically used in turbine engines because synthetic oils retain their lubricating properties and are more resistant to oxidation at high temperatures. These oils also have better characteristics concerning thermal stability and the viscosity. The oils used for turbine engines are required to operate over a wide range of temperatures. Temperatures from -40°C to +250°C for bearing temperatures have to be foreseen. Today, oil of the fourth generation of synthetic oils is available. According to the development generation the oils are designated as Type 2, Type 3 or Type 4 oils. Type 2 oils are still available and in use. The main characteristics of engine oil are:

• Viscosity • Pour point • Flash point • Pressure resistance • Oxidation resistance • Thermal stability

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CHAPTER 2. LUBE SYSTEM DESCRIPTION AND MODEL DEVELOPMENT Viscosity

The viscosity is the most important characteristic of engine oil. It is commonly perceived as “thickness” or resistance to flow. Viscosity describes a fluid’s internal resistance to flow and may be thought of as a measure of fluid friction. The viscos-ity µ of the oil depends on the temperature of the oil. It is high at low temperatures and vice versa. This means that warm oil with a low viscosity has a low internal resistance. A low internal resistance is an advantage, but if the viscosity gets too low, the load carrying capability of the oil decreases and the oil film can no longer separate the moving surfaces. Thus the lubrication capability is no longer ensured. The cinematic viscosity ν is usually measured in centistokes (cS) and is linked to absolute viscosity through the relationship µ = ρν. The cinematic viscosity of a typical Type 3 oil is around 5.3 · 10−6m2/s at 99° C and higher than 0, 012m2/s at a temperature of 40° C.

Pour Point

The pour point of the oil is reached if it is cooled down to a temperature at which the oil becomes so thick that it stops flowing. Typical Type 3 oils for jet engines have a pour point of 62° C (-80°F). Thus, if the temperature is lower, the oil stops to flow.

Flash Point

The flash point of a flammable liquid (here engine oil) is the lowest temperature at which it can form an ignitable mixture with air. It should be as high as possible to avoid fire in the oil system. Typical Type 3 oils have a flashpoint higher than 250° C (482°F).

Pressure Resistance

The pressure resistance or load carrying capability is an important factor for the formation of an oil film between the moving parts. This film resists the loads on the moving surfaces of bearings and gears and prevents contact between the sur-faces. If the loads are higher than the pressure resistance capability of the oil, the surfaces come into contact and heavy material wear occurs. A typical value for a Type 3 oil is 475, 5 · 106_N/m.

Oxidation Resistance

Oxidation is the reaction between oil and oxygen. When the oil reacts with oxy-gen it gets thicker and increases its viscosity due to the formation of acids and sludge. This reaction reduces the lubrication capability of the oil. The reaction

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CHAPTER 2. LUBE SYSTEM DESCRIPTION AND MODEL DEVELOPMENT rate with oxygen increases when the oil temperature and the extent of contamina-tion increase. Therefore the oxidacontamina-tion resistance is an important characteristic of oil because it influences the durability of the oil. Typical Type 3 oils are resistant to oxidation at oil temperatures up to 220° C (428°F).

Thermal Stability

The thermal stability describes the resistance of the oil to decomposition of the oil compounds at high temperatures. The oil molecules are made of several indi-vidual compounds. At high temperatures these molecules can break apart and the chemical composition and the lubrication capability of the oil changes. This decom-position usually occurs at very high temperatures, well above the normal operating temperatures of the engine oil. Type 3 oils can resist chemical decomposition at temperatures of up to 340° C (662°F).

2.1.4 Accumulator Tank

The oil of the lubrication system is stored in a tank. To allow servicing, devices for filling and draining the oil tank are provided. For the check of the oil level a sight glass or dipstick is installed. For the remote indication of the oil level an electrical quantity sensor is located in the oil tank. The recirculatory system generally provides two different locations for the oil coolers in the system. If the oil is returned from the sumps directly to the tank without cooling, the system is called a hot tank system. If the oil passes the oil cooler before it enters the oil tank, the system is called a cold tank system. Typical locations for the oil tanks on the engine are either the fan case or the accessory gearbox. If the engine has a core engine-mounted accessory gearbox with an oil tank, the access to the oil tank for servicing is not as good as the access to a fan case-mounted oil tank. The oil tank of the PW4000 for example requires an access door in the inner barrel of the thrust reverser structure because this oil tank is mounted on the gearbox of this engine. This variant is possible on engines with short duct nacelles only. A fan case-mounted oil tank can be used on every engine design. The typical oil tank has three connections to the lubrication system. These are the oil supply line to the pressure oil pump, the oil return line from the scavenge pumps and the vent line. The scavenge pumps deliver a scavenge oil/air mixture into the tank. This air is vented through a static de-oiler within the tank to the de-oiler or into one of the bearing compartments. On some oil tanks a pressurization valve is installed in the vent line connection. This valve keeps an air pressure slightly above the ambient pressure in the tank after engine shutdown. This facilitates the

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CHAPTER 2. LUBE SYSTEM DESCRIPTION AND MODEL DEVELOPMENT oil supply to the pressure pump during engine start. For the remote sensing of the oil quantity a sensor is installed in the oil tank and connected to the assigned computer. The oil tank can be filled directly with oil through the fill port or via remote fill connections. To check the oil level a sight glass is installed in the oil tank wall. If the pressure fill ports are used for refilling the oil tank, the oil is pumped into the tank until it is visible in the overflow hose.

2.1.5 Hydraulic Pump and Filters

Figure 2.5: Cutaway of a typical double stage oil pump.

The oil pumps used in lubrication systems are gear type pumps or vane pumps. The gear type pumps are of the classic type with parallel shafts or they are of the gerotor type with coaxial gears. Usually one pressure pump and for each sump one scavenge pump are used in a lubrication system. The magnetic chip detectors for debris monitoring are installed in the scavenge pump inlets or in the scavenge oil lines upstream of the pumps where easy access is ensured. The filter system is a very important element for the reliability of a recirculatory lubrication system. Because the oil has to pass through small holes and passages, even very small particles contaminating the oil could block the oil flow resulting in a lubrication failure. The normal contaminant is abrasive material and is released by the bearings and gears during their normal operation. It is flushed away from the bearings and gears by the oil and carried with the scavenge oil flow away from the sump. In the filters of the system the contaminants are removed nearly completely from the oil. Thus the oil can be supplied again to the bearings and gears. If a bearing or gear failure develops, larger than normal particles will be found in the filters and on the magnetic chip detectors. A classic filter arrangement in a lubrication

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CHAPTER 2. LUBE SYSTEM DESCRIPTION AND MODEL DEVELOPMENT system is one pressure filter downstream of the pressure pump and one scavenge filter downstream of the scavenge pump. In this arrangement the scavenge filter has the finest filter element. Also in use are systems with one filter in the pressure system only. In these systems a back-up filter is installed to ensure oil filtering if the main filter is clogged. Every oil filter is equipped with a bypass valve to sustain the oil flow while the filter element is clogged. The filter elements used in the oil filters have a mesh size between 15 and 65 microns. The finest filter in the system is monitored with a differential pressure switch for clogging. The resulting clogging warning informs the flight crew about the limited filtering efficiency in the system. In some systems additional filter screens are installed upstream of the oil nozzles in the supply lines. These screens are called last chance screens. They prevent a clogging of the oil nozzles by particles that can reach the nozzles if the filter bypass valve is open.

2.1.6 Oil Cooler

Figure 2.6: A Low-Pressure fuel-cooled oil cooler [3].

During the lubrication process heat is transferred from the engine components to the oil. It has subsequently to be removed from the oil to keep the oil

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temper-CHAPTER 2. LUBE SYSTEM DESCRIPTION AND MODEL DEVELOPMENT ature within the set limits. This requires the installation of an oil cooler in the system. The cooling medium may be fuel or air and in some designs a combination of a fuel-cooled and an air-cooled heat exchanger is used. The cooler may be lo-cated either on the feed side or the return side of the lubrication system resulting either in a hot tank system or a cold tank system. The typical oil cooler used on turbofan engines is the fuel-oil heat exchanger. It has a smaller volume compared to an air-oil heat exchanger of the same cooling capacity and the use of fuel as the cooling medium results in a heating of the cold fuel delivered by the aircraft fuel system. The fuel-oil heat exchanger is also effective during ground operation and need not to be exposed to the airflow. The lubrication systems on some engines use additional air-cooled oil coolers to control the temperatures of oil and fuel during the operation with low fuel flows. In some fuel-cooled oil coolers a thermostatic by-pass valve is installed. It maintains a proper oil temperature by varying the portion of the oil passing, respectively bypassing, the oil cooler. This valve allows changes to the cooling effect in response to the changes in fuel flow in different phases of engine operation. All other oil cooler designs have a bypass valve responding to the differential pressure across the cooler. The highest differential pressure develops with the coldest oil. Thus the cooler is bypassed when the oil temperature is low.

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2.1.7 Lube System Hydraulic Scheme

Figure 2.7: Gearbox oil system reduced.

In Fig.(2.7) we can find the oil system scheme and as you can see it is as-sembled by the main components which have been described before. It has to be clarified that the word ”gearbox” represented in the figure means a control volume including all the rotative parts (gears, bearings, ecc...) but every other part, like pipes, pumps,tank and bypass valve are contained in the ”gearbox” intendend as the physical case except for the cooler which stands outside. Practically speaking the gearbox physical boundaries are the valve ”GBX to COOLER” and ”COOLER to GBX”. Moving forward, in this system the accumulator tank contains the lubri-ficant which recirculate in the circuit. The oil is pumped from the tank towards the gearbox and, in certain conditions, such as overpressure in the delivery line, flows

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CHAPTER 2. LUBE SYSTEM DESCRIPTION AND MODEL DEVELOPMENT through the bypass valve returning in the accumulator tank. Once in the gearbox it lubrificates all the rotating parts and ends down in the sump. The scavenge pump, once again, moves the oil towards the Fuel-Cooled Oil-Cooler which could be by-passed in case cooler is clogged, or if the oil temperature is too low.

2.2 Testing Activities

2.2.1 Test Rig Description and Measurements Available

The test rig receive the input given by the operator through the consolle. These inputs regulate the PTO shaft velocity, the starter angular velocity and the oil temperature.

The experimental data acquired during the tests involve temperatures, pressures and angular velocity of the PTO, these have been named as follows:

• Tic: Cooler inlet temperature;

• Toc: Cooler outlet temperature;

• ∆Pdelivery: Pressure rise caused by the delivery pump;

• ∆Pscavenge: Pressure rise caused by the scavenge pump;

• ∆Pgearbox: Pressure drop caused by the gearbox;

• ∆Pcooler: Pressure drop caused by the cooler;

• ωP T O: Angular velocity of the PTO.

This physical quantities were collected by the Data Acquisition System (DAS) at the frequence of 1 Hz and are represented in section 2.2.3.

2.2.2 Acceptance Test Description

During the Acceptance Test, the operator manage the PTO shaft speed through a potentiometer and the temperature by setting the value that has to be reached in a numbered column. Specifical combinations of angular velocity and temperature are representative of different flight conditions that have to be simulated. In the second phase of the test the engine starting has to be simulated therefore an electric mandrel provides the motion to the gearbox through the air turbine starter input drive. Also in this case, the operator manage the electric mandrel angular speed through a potentiometer. Actually, in the engine starting condition the Auxiliary

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CHAPTER 2. LUBE SYSTEM DESCRIPTION AND MODEL DEVELOPMENT Power Unit (APU) provides the motion to both the starter and the PTO. During the PTO motion condition the gearbox rotates at different percentage of its max-imum angular speed. For every velocity steady condition, the physical quantities monitored has to be in a specific safe range. If any of these quantities results out of range, the consolle gives an alarm and the test is stopped.

2.2.3 Complete Experimental Data

In this section the complete data acquired during the test are represented. For confidential reasons they all have been normalized respect to their maximum value.

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Figure 2.9: System pressure drops complete experimental data.

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Figure 2.11: Temperatures complete experimental data.

As it can be seen from Fig.(2.8) to Fig.(2.11) the test lasts more than one hour. In Fig.(2.8) the PTO dynamics is represented: an idle condition is mantained for the first 500 sec. of the test; this time allows the oil to circulate in the gearbox and permits to refill the tank untill it is completely full. At this time, the test starts again and the operator reaches and mantain respectively the 60%, 80%, 100% and 105% of ωpto. Each one of this phases has specifical requirements on the values of

the physical quantities measured during the test.

2.2.4 Useful Experimental Data

Starting from the experimental data shown above have been decided to focus on the first phase of the test. The phase starts from the idle condition and ends when the PTO reaches the 60% of its maximum angular speed. This has been done to understand how the physical quantities initially evolve. Therefore the same plots are shown with a temporal zoom of the phase of interest:

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Figure 2.12: ωpto useful experimental data.

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Figure 2.14: Pump pressure rise useful experimental data.

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2.3 System Modelling

2.3.1 Model Assumptions

The model, as it has been introduced before, needs some reductions in order to make it easier to implement on the Simulink software. The major assumptions that have been made are the following:

• The oil density remains constant during the simulation, therefore the liquid is considered incompressible.

• The oil viscosity does not change with the temperature. • The heat transfer coefficient Cp remains constant.

• In the law of the conservation of energy the terms regarding the cinetic and potential energy have been considered negligible for the nature of the system itself: there are not large differences in height to make the potential energy considerable and, also for the cinetic energy, the speed of the oil flow through the inlet and the outlet of the control volumes remains the same.

• The tank temperature Tt has been assumed identical to the temperature at

the inlet of the gearbox Tig. In the same way the temperature at the outlet

of the gearbox Tog has been assumed identical to the temperature at the inlet

of the cooler Tic; this has been possible neglecting the temperature increase

due to the pump.

• The oil flow through the bypass-valves has been assumed equal to zero. The condition ∆p ≥ ∆pthreshold is not reached during all the simulation.

• Since the pressures of the tank and the outlet of the gearbox change only slightly compare to the other differential pressures, they have been kept at a constant value as it can be seen in Fig. (2.11).

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Figure 2.16: Constant approximation for the pressures Pt and Pog

2.3.2 Reduced Hydraulic Scheme

Figure 2.17: Gearbox oil system reduced.

Fig.(2.17) is rapresentative of the assumptions made in section 2.3.1 and shows the three control volumes in which the system has been divided in order to write

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CHAPTER 2. LUBE SYSTEM DESCRIPTION AND MODEL DEVELOPMENT the model equations. This three control volumes have been associated to the main thermal inertias of the system:

• Tank; • Gearbox; • Cooler.

In addition to this, the variables of the model have been introduced highlitghting the location of every physical quantity represented.

2.3.3 Model Equations

Jptoω˙pto= ηptoMpto− Kf b(Pig − Pog) − C0 − C1ωpto− Mpump (2.1)

where :

Mpump = Ddel(Pig − Pt) + Dsca(Pic− Pog) (2.2)

1

2mtCp( ˙Toc+ ˙Tig) = Qcooler(Poc+ ρCpToc) +

Ddel(Pig − Poc)ωptoτpump

ηpto

− Qingbx(Pig + ρCpTig) (2.3)

1

2mgbxCp( ˙Tig + ˙Tic) = Qingbx(Pig+ρCpTig)+

Dscav(Pic− Pig)ωptoτpump

ηpto

+C0ωpto+C1ωpto2 −Qcooler(Pic+ρCpTic)

(2.4)

1

2mcoolerCp( ˙Tic + ˙Toc) = Qcooler[(Pic − Poc) + ρCp(Tic − Toc)] − ˙Wcooler (2.5) Pig − Pog = 2µQingbx D3 gbxδ2 (2.6) Pic− Poc= 2µQcooler D3 coolδ2 (2.7)

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CHAPTER 2. LUBE SYSTEM DESCRIPTION AND MODEL DEVELOPMENT Qbp1 =      0 if Pic− Poc < ∆pthreshold Cd1 r 2 ρAbp1 √ Pic− Poc if Pic− Poc ≥ ∆pthreshold (2.8) Qbp2 =      0 if Pig− Pt< ∆pthreshold1 Cd2 r 2 ρAbp2pPig− Pt if Pig− Pt≥ ∆pthreshold2 (2.9)

Qdelivery= ωptoτpumpDdel (2.10)

Qscavenge = ωptoτpumpDscav (2.11)

Qleak = Kleakage(Pig− Pt) (2.12)

Qingbx = Qdelivery− Qleak (2.13)

Qcooler = Qscavenge+ Qleak (2.14)

The PTO dynamics (Eq.(2.1)) is regulated by the equilibrium of the torques involved in the system. To make it as clear as possible, we have a PTO input Torque which generates an angular acceleration and obviously an angular velocity of the shaft. This shaft transmits the motion to the gearbox iself but also provide the angular velocity necessary to the pump that generates the flow, both for the delivery and for the scavenge line. So we already introduced two dissipative con-tributes of the input torque which are related to it, through an efficiency coefficient ηpto. For the loss of information regarding the system parameters value a system

identification approach has been followed.

The torques of the delivery and scavenge stages (Eq.(2.2)) of the pump is given by the product of the respective displacement and pressure rise across the inlet and outlet of the pump.

For the temperature and pressure dynamics have been choosen different control volumes in the lubrication system, as shown in Fig.(2.17), including the three prin-cipal thermical inertias: the tank, the cooler and the gearbox. The first differential equation (Eq.(2.3)) is written considering the conservation of energy law of the system from the inlet of the tank to the inlet of the gearbox, including the delivery stage of the pump.

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CHAPTER 2. LUBE SYSTEM DESCRIPTION AND MODEL DEVELOPMENT inlet of the cooler including the work of the scavenge stage of the pump and the heat generated by friction and dissipative mechanisms in the gearbox.

Finally the third thermical inertia taken in consideration is the cooler (Eq.(2.5)), where we find his contribution to the heat absorption.

In Eq. (2.3), (2.4) and (2.5) the temperature of every thermical mass has been written as the mean value of the temperatures at the inlet and the outlet of the control volume. Concerning the pressure and the mass flow dynamics a laminar flow model has been adopted since the Reynolds Number resulting is < 4000 in every section of the circuit. The pressure rise across the pump and pressure drops in the gbx and the cooler are given by Eq.(2.6) and Eq.(2.7):

As expected from a laminar model of the mass flow, the relation between Q and ∆p is linear. As we can see in Fig.(2.7) two Bypass Valves are part of the lubrication system, therefore the massflow through them could be represented as in Eq.(2.8) and Eq.(2.9). Finally for the massflow behaviour we can refer to a scheme representing the oil circuit and the pump model, as can see in Fig. (2.10):

Figure 2.18: Pump modeling and oil massflow circuit representation.

As it can be seen in the figure the Scavenge stage of the pump receive both the flow coming from the gearbox and the leakage of the delivery stage, once the displacement of the stages is known the massflow in every section of the circuit is known Eqs.(2.10-2.14). Concerning the inputs of the model we have:

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CHAPTER 2. LUBE SYSTEM DESCRIPTION AND MODEL DEVELOPMENT • The PTO torque Mpto;

• The heat absorption rate of the cooler ˙Wcooler.

In this way the system model is completely defined, in the following section the author will introduce the implementation of the model on the software Simulink.

2.4 Model Implementation in the Matlab/Simulink

Environment

2.4.1 Configuration Parameters

In Tables (2.2), (2.3)and (2.4) are respectively represented the time simulation parameters set, the thermodynamic quantities of interest that has to be assumed and the model input values:

Simulation duration time ∆tsimu= 120sec.

Fixed step size ∆tstep= 0.01.

Input start time tstep = 1sec.

Solver ode4(Range − Kutta)

Table 2.1: Simulation configuration parameters.

The simulation fixed step size has been set to 0.01 sec. to ensure accurate re-sults that match the expectations, as based on experimental data. In addition to this, the model results fast enough to be considered real-time capable.

Simulink provides two types of fixed-step continuous solvers-explicit and implicit. An implicit solver requires more computation per step than an explicit solver but is more stable. Therefore, the implicit fixed-step solver is more adept at solving a stiff system than the fixed-step explicit solvers. Since the system modelled is not considered a stiff model rather relatively simple, an explicit solver has been used. Simulink provides a set of fixed-step continuous explicit solvers which differ in the specific numerical integration technique that they use to compute the state deriva-tives of the model, from the least complex (ode1) to the most complex (ode8). Also, for any given step size, the more computationally complex the solver is, the more accurate are the simulation results. The best compromise between computational speed and accurate results have been reached with the Fourth-Order Runge-Kutta (RK4) formula.

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2.4.2 Model Parameters and Initial Conditions

The non linear model introduced has been developed to reproduce the bea-haviour of the physical quantities involved during a specifical phase of an accep-tance test of a gearbox in general. The experimental data are real data acquired during tests, but due to the lack of informations regarding the machine and its main components a preliminary system identification has been used. The model developed simulate the first phase of the acceptance test, let’s clarify what happens in this phase: The simulated phase is 120sec. long; during this time the PTO gives an input torque (values have been extrapolated from a look up table and reported in Fig.(2.12)) starting from an idle condition where it rotates at the 40% of its maximum angular velocity. The motion is transmitted to the gearbox and to the pump. So an equilibrium condition has to be satisfied during the idle. In Table (2.2) are reported the initial value of the sperimental data:

PTO angular speed ωpto(0) = 345 rad/sec

Temperature at the cooler inlet Tic(0) = 56.68◦C

Temperature at the cooler outlet Toc(0) = 40.55◦C

Gearbox pressure drop ∆pgbx(0) = 0.0409 bar

Cooler pressure drop ∆pcooler(0) = 0.0915 bar

Delivery stage pressure rise ∆pdel(0) = 0.3449 bar

Scavenge stage pressure rise ∆pscav(0) = 7.17 · 10−4bar

Table 2.2: Initial values of the sperimental data

in Fig.(2.19) is represented the PTO Torque related to its angular speed nor-malized with respect its maximum value:

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CHAPTER 2. LUBE SYSTEM DESCRIPTION AND MODEL DEVELOPMENT The Mpto input is given to the system by a step with initial value ωpto(0)/ωpto∞

and final value equal to 1. The step enters in a look up table representetd in Fig (2.19) which generates the value of Mpto during the simulation as it can be seen in

Fig.(2.20):

Figure 2.20: Generation of the input Mpto for the simulation.

In Tables (2.3)and (2.4) are respectively represented the thermodynamic quan-tities of interest that has to be assumed and the model input values:

Oil Density ρ = 830 Kg/m3

Oil Viscosity µ = 0.0138 Kg/(ms)

Heat transfer coefficient Cp = 2093 J/(Kg◦C)

Table 2.3: Thermodynamic quantities value.

Initial PTO Torque Mpto0 = 5 N m

Final PTO Torque Mpto∞ = 150 N m

Initial Cooler heat rate absorption W˙cooler0= 0

Final Cooler heat rate absorption W˙cooler∞ = 4KW

Table 2.4: Input Values

As we can see in Table (2.4) the term ˙Wcooler is initially equal to zero.

Once the input is given, the model moves from the initial equilibrium condition to the final one through a transitory phase. The parameters obtained by the two equilibrium conditions will be illustrated in detail in the Chapter 3.

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2.4.3 Simulink Block Diagrams

Figure 2.21: Simulation Model.

Through the clock block the simulation time is generated while the Load Data button calls back a MatLab file which load all the parameters values obtained by the equilibrium conditions. The MatLab file is reported in Appendix A. In the Shaft Dynamics block we find the Eq. (2.1), as can be seen in Fig.(2.22), representing the time trend of ωpto through the simulation:

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CHAPTER 2. LUBE SYSTEM DESCRIPTION AND MODEL DEVELOPMENT In the ”Pressure Dynamics and Oil Flow” Block are inserted the equations regarding pressure and oil mass flow. Observing the Eq.(2.6) and Eq.(2.13) we note a reciprocal dependency between the two quantities Pig and Qingbx, for this

reason has been necessary to write an explicit equation for Pig which has been

located in the block ”Pig Pressure” (see Fig.(2.23)). The equation is in the form:

Pig = ( 2µ(Qdel+ KleakagePt) D3 gbxδ2 + Pog) 1 (1 + 2µKleakage D3 gbxδ2) (2.15)

Figure 2.23: Pressure dynamics and oil Simulink block diagram.

The ”Temperatures dynamics” Block is divided into three other sub-Blocks where are respectively located Eq.(2.3), (2.4) and (2.5). They are showed in Fig.(2.24):

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Figure 2.24: Temperatures dynamics block diagram.

Figure 2.25: Tig Simulink block diagram.

In the figure above we can see that the temporal trend of the temperature Tig

depends on the contributes to the internal energy which could increase or decrease. In this case we have three different terms. On one hand, the first one is related to the mass flow rate and the enthalpy entering the control volume, this produce a positive effect directly proportional to the quantities Qcooler,TocandPoc. On the

other hand we have the mass flow rate and enthalpy leaving the control volume which generate a negative effect proportional to Qingbx,Pig and Tig itself. Moreover

we have an introduction of energy due to the delivery stage of the pump which is always positive and partecipates to the temperature increase. During the evolution of the transitory the thermal mass mt plays a significant role, since it influences

the rate of change of the temperature. Practically speaking, larger mass needs more energy to increase its temperature. Finally, another negative contribute to

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CHAPTER 2. LUBE SYSTEM DESCRIPTION AND MODEL DEVELOPMENT ˙

Tig is given by the term ˙Toc which behaviour is showed in Fig. (2.28) and will be

discussed later.

Figure 2.26: Tic Simulink block diagram.

In this case, in addition to the contributes related to the enthalpy entering and leaving the control volume considered and the power introduced by the scavenge pump action, we can see other two terms which are inserted to represent the tem-perature rising inside the gearbox due to the friction losses and other dissipation mechanisms. With the term C0ωpto we are considering the power introduced in the

control volume due to all the components which rotate inside the gearbox, there-fore C0 represent a constant resistence torque that oppose the motion of the PTO.

The second term represent the power introduced by a torque C1ωpto which is not

constant, but increase linearly with the PTO shaft angular speed. This is intro-duced as a major contribution to the temperature increase inside the gearbox since the power is related to ωpto through a quadratic proportionality. This dissipative

"Development of experimentally-validated models of gearbox lubrication systems for the health-monitoring of aircraft engines"

Universit`

a di Pisa

Development of

experimentally-validated models of

gearbox lubrication systems for the

health-monitoring of aircraft engines

Abstract

Contents

Lista dei Simboli

List of Figures

List of Tables

Lista degli Acronimi

Introduction

Chapter 1

Virtual-Testing and

Health-Monitoring of Aircraft

Systems

1.1

The Engine F124-GA-100

1.2

Health-Monitoring of a Wind Turbine

1.3

Blade Health Monitoring and Diagnosis Method

of Wind Turbine

1.4

Landing Gear Health Monitoring

1.5

Physics-based prognostics

Chapter 2

Lube System Description and

Model Development

2.1

Accessory Gearbox

2.1.1

Basic Requirements

2.1.2

Lubrication Circuit

2.1.3

Fluid Properties

2.1.4

Accumulator Tank

2.1.5

Hydraulic Pump and Filters

2.1.6

Oil Cooler

2.1.7

Lube System Hydraulic Scheme

2.2

Testing Activities

2.2.1

Test Rig Description and Measurements Available

2.2.2

Acceptance Test Description

2.2.3

Complete Experimental Data

2.2.4

Useful Experimental Data

2.3

System Modelling

2.3.1

Model Assumptions

2.3.2

Reduced Hydraulic Scheme

2.3.3

Model Equations

2.4

Model Implementation in the Matlab/Simulink

Environment

2.4.1

Configuration Parameters

2.4.2

Model Parameters and Initial Conditions

2.4.3

Simulink Block Diagrams