Aircraft tires health-management: development of models for diagnosis and prognosis of faults via on-ground dynamic simulation.

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Università di Pisa

Dipartimento di Ingegneria Civile e Industriale

Tesi di Laurea Magistrale in Ingegneria Aerospaziale

Aircraft tires health-management: development of

models for diagnosis and prognosis of faults via

on-ground dynamic simulation.

Relatori: Candidato: Prof. Ing. Gianpietro Di Rito Kayleigh Baldanzi Prof. Ing. Roberto Galatolo

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A Marco, che mi ha sempre detto che sono in grado di fare ogni cosa.

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Abstract

This thesis is part of the research activities carried out at the Aerospace Division of Dipartimento di Ingegneria Civile ed Industriale dell’Università di Pisa, for the development of the landing/roll-out simulator of a light jet aircraft. The main objective of the simulator is to investigate the potentialities and the limitations of implementing automatic control functions for the directional control of small aircrafts on ground, through the combined use of conventional commands (steering and rudder) and hydraulic differential brakes as stand-by command. The first section of the work is focused on characterisation of failure transients of the fault-tolerant directional control, after a nose wheel steering jamming, before the differential brakes are activated to compensate the fault, with the objective of identifying the requirements for a safe and effective ground directional control. In the second part, a physical-based model for tires’ faults, including heat generation and wear, is developed and implemented in the simulator, in order to estimate the Remaining Useful Life of the component. Finally, a Prognostic Health Management model, that could actually been used in the operative aircraft, is developed and verificated.

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List of Figures

Figure 1.1 - Impact of maintenance strategies on costs [1] . . . 2

Figure 1.2 - Benefits of diagnostics and prognostics [2] . . . 4

Figure 1.3 - Escalation of scheduled maintenance tasks [1] . . . 6

Figure 1.4 - Classification of prognostic approaches [1] . . . 6

Figure 1.5 - SAT [3] . . . 8

Figure 1.6 - Basic architecture of the directional control laws . . . 12

Figure 1.7 - Reference aircraft details [12] . . . 13

Figure 1.8 - The development of a skid by on-and-off brake application . . . 14

Figure 1.9 - Antiskid closed loop . . . 15

Figure 1.10 - Influence of nose steering, differential brakes and rudder on ground directional control . . . 16

Figure 1.11 - Fatal Accidents and Onboard Fatalities by Phase of Flight . . . 17

Figure 1.12 - Fatalities by CICTT Aviation Occurrence Categories [4] . . . 18

Figure 1.13 - Most important causal factors for landing veer offs [15] . . . 19

Figure 1.14 - Veer off landing (4 March 2011, Nuuk, Greenland) [16] . . . 20

Figure 2.1 - Qualitative trend of the braking force with the apparent wheel slippage [18] . . . 21

Figure 2.2 - Tire dynamics . . . 22

Figure 2.3 - Slip Angle . . . 23

Figure 2.4 – Longitudinal and lateral friction coefficients in function of the slip ratio with increasing slip angle [18] . . . 24

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Figure 2.5 - Longitudinal and lateral friction coefficients in function of the slip ratio and

slip angle for wet and dry runway condition [18] . . . 25

Figure 1.6 – Comparison between Dugoff model and Pacejka model [8] . . . 27

Figure 2.7- Example, force representation by Magic Formula . . . 29

Figure 2.8- Comparison between Dugoff Model an Pacejka Model, dry runway . . . . 30

Figure 2.9 - Comparison between Dugoff Model and Pacejka Model, wet runway . . 31

Figure 2.10 – Comparison between Dugoff Model and Magic Formula for the nose steering, dry runway . . . 33

Figure 2.11 – Comparison between Dugoff Model and Magic Formula for the nose steering, wet runway . . . 33

Figure 2.12 – Comparison of aircraft velocity, dry runway . . . 34

Figure 2.12 – Comparison of aircraft velocity, wet runway . . . 34

Figure 3.1 – Temporal evolution of the thrust . . . 36

Figure 3.2 – Temporal evolution of the bump gusts . . . 37

Figure 3.3 – Temporal evolution of the constant gust . . . 38

Figure 3.4 – Failure injection and time of latency . . . 39

Figure 3.5 – Landing roll-out simulator . . . 40

Figure 3.6- Yaw Moments, Bump gust & Dry runway . . . 43

Figure 3.7- Yaw Moments, Costant gust & Dry runway . . . 43

Figure 3.8- Yaw Moments, Bump gust & Wet runway . . . 44

Figure 3.9- Yaw Moments, Costant gust & Wet runway . . . 44

Figure 3.10 - Aircraft trajectory, only Rudder. Dry Runway and Constant Gust . . . .46

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Figure 3.12 – Aircraft trajectory, only steering. Dry Runway and Constant Gust . . . . 47

Figure 3.13 – Yaw Moment, only steering. Dry Runway and Constant Gust . . . 47

Figure 3.14- Aircraft trajectory, Differential Brakes. Dry Runway and Constant Gust . 48 Figure 3.15-Yaw Moment, only differential brakes. Dry Runway and Constant Gust . 48 Figure 3.16 - Aircraft trajectory, Steering and Differential Brakes. Dry Runway and Constant Gust . . . 49

Figure 3.17 – Yaw Moment, steering and differential brakes. Dry Runway and Constant Gust . . . 49

Figure 3.18 – Steering angle time response, with dry runway and constant gust . . . . 53

Figure 3.19 – Yaw moment, Latency 0 msec . . . 54

Figure 3.20 - Yaw moment, Latency 150 msec . . . 55

Figure 3.24- Aircraft trajectory with increasing latency, compared to the trajectory with no steer failure. Constant gust and dry runway . . . 58

Figure 3.25 - Bar graph of nondimensional yaw moment and time locked wheel for various latency times . . . 59

Figure 3.26 – Bar graph of nondimensional yaw moment and time locked wheel for various latency times, higher range . . . 59

Figure 3.27 - Aircraft trajectory with increasing latency, compared to the trajectory with no steer failure, with constant gust and wet runway . . . 61

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Figure 4.2 This occurs when the tire stops rotating while the aircraft is still moving. The

runway grinds off rubber and fabric as the tire is dragged along the surface . . . 63

Figure 4.3- Example of Goodyear tire [23] . . . 64

Figure 4.4- Tire section and fundamental dimensions definition [23] . . . 64

Figure 4.5- Radial ply aircraft tire construction [23] . . . 65

Figure 4.6 - Groove depth [24] . . . 66

Figure 4.7 - Contact area, Boeing formulation . . . 67

Figure 4.8 - Boeing 737 nose tire footprint; 215 psi; 10000 lb [27] . . . 68

Figure 4.9-Volume involved in the heat exchange in function of the slip ratio . . . 72

Figure 4.10– Tire hardness vs Temperature . . . 72

Figure 4.11– Brinnel-Shore A hardness correlation . . . 73

Figure 4.12 -Variation of tire wear rate with slip ratio on test runways [31] . . . 74

Figure 4.13- Tire temperature, symmetrical braking . . . 78

Figure 4.14 – Peak of temperature at the touchdown . . . 79

Figure 4.15– Maximum temperature at touchdown, ANSYS simulation. [25] . . . 79

Figure 4.16 – Heat, Symmetrical Braking . . . 80

Figure 4.17– Volume removed, symmetrical braking . . . 81

Figure 4.18 – Wear Rate, symmetrical braking . . . 81

Figure 4.19 - Tire temperature, Bump Gust . . . 82

Figure 4.20 - Tire volume removed, Bump Gust . . . 82

Figure 4.21- Tire temperature, Constant Gust . . . 83

Figure 4.22- Tire volume removed, Constant Gust . . . 83

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Figure 4.24 - Tire volume removed, Constant Gust and Failure . . . 84

Figure 4.25 – Tire wear results compared for wet and dry runway . . . 86

Figure 4.26 - Scheme of the PHM model . . . 89

Figure 4.27 - ( ) with Pacejka model . . . 90

Figure 4.28 - Volume removed in % of critical volume and RUL estimation . . . 92

Figure 4.29 – Zoom of the first 300 cycles, RUL estimation with different weather condition histories . . . 93

Figure 4.30 – RUL estimation with differents weather condition histories . . . 94

Figure 4.31 – RUL estimated at subsequents maintenance checks . . . 95

Figure 4.32 – Comparison of RUL between simulation results and PHM model . . . 96

Figure A1- Aircraft trajectory, only rudder. Dry Runway and Bump Gust . . . 98

Figure A2- Yaw Moment, only rudder. Dry Runway and Bump Gust . . . 98

Figure A3- Aircraft trajectory, only steering, Dry Runway and Bump Gust . . . 99

Figure A4 - Yaw Moment, only steering. Dry Runway and Bump Gust . . . 99

Figure A5 - Aircraft trajectory, only differential brakes. Dry Runway and Bump Gust . . . . . 100

Figure A6 – Yaw Moment, only differential brakes. Dry Runway and Bump Gust . . . 100

Figure A7 - Aircraft trajectory, steering and differential brakes. Dry Runway and Bump Gust . . . 101

Figure A8 – Yaw Moment, steering and differential brakes. Dry Runway and Bump Gust . . . . . . 101

Figure A9 - Aircraft trajectory, only steering. Wet Runway and Bump Gust . . . 102

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Figure A11 - Aircraft trajectory, only differential brakes. Wet Runway and Bump Gust . . . . 103 Figure A12- Yaw Moment, only differential brakes. Wet Runway and Bump Gust . . 103 Figure A13- Aircraft trajectory, only steering. Wet Runway and Constant Gust . . . . 103 Figure A14- Yaw Moment, only steering. Wet Runway and Constant Gust . . . 104 Figure A15- Aircraft trajectory, only differential brakes. Wet Runway and Constant Gust . . . 105 Figure A16- Yaw Moment, only differential brakes. Wet Runway and Constant Gust . . . . . . 105

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List of Tables

Table 1.1 - Aircraft aeromechanical characteristics [12] . . . 13

Table 2.1 - Coefficients of Pacejka Model . . . 30

Table 3.1 - Single command axis simulation results . . . 50

Table 3.2 – Summary of results with increasing latency . . . 57

Table 3.3– Summary of results, increasing latency, wet runway . . . 60

Table 4.1- Tire technical features . . . 65

Table 4.2- Material parameters of tire tread . . . 66

Table 4.4- Total volume worn out in each simulation . . . 87

Table 4.5 – Summary of PHM results . . . 90

Table 4.6 – Percentage of landing conditions for a jet life . . . 92

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Introduction

This thesis analyses the performances of a light jet aircraft during the landing roll-out phase (from the touchdown to the taxing condition) through a flight simulator. The purpose is to develop and verificate a prognostic healt-management model for the tires, as well as identify the requirements for a safe and performant directional control of the aircraft on ground, after a diagnostic analysis of faults. In the first chapter we point up the importance of diagnosis and prognosis for maintenance enhancement, we explain the choice of the study case taken in account, according to the trend for the future of air transport, as well as describe the landing roll-out simulator utilised. In the second chapter various tire loads models are compared and the one that better represents the physical behaviour of the tires is implemented in the flight simulator. The third chapter analyses the transient that occurs after a steering failure, in a steering and differential brakes in active/stand-by configuration, and identifies the requirements, in terms of time of latency, of the failure transitory. In the last chapter a physical model, that includes wear mechanism and heat generation, for the prognosis of the tire, is developed and implemented in the simulator. Afterwards, a prognostic health-management model is developed and compared with the simulations results. Finally the Remaining Useful Life of the tires is estimated.

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Chapter 1

Aircraft systems reliability and safety

enhancement via modelling and simulation

"Safety and reliability are air transport’s top priorities." [1]

In the history of aviation, the increase of safety has always been the main goal and doing it with the minimum costs has always been the challenge. Hence, the importance to study new methods, with the help of physical models implemented in an aircraft flight simulator, to monitor the aircraft systems health in order to prevent the failures and develop an intelligent maintenance that minimizes costs and time.

1.1 Safety and maintenance in civil aviation

Aircaft maintenance forms a significant part of an aircraft’s airworthiness criteria, with the key objectives to ensure a fully-serviced, operational and safe aircraft. Poor maintenance can have a variety of impacts to an aircraft, its crew and its passengers. Delays to aircraft dispatch time could cause a financial impact to the airline (runway charges) and customer dissatisfaction. In more severe cases, poor maintenance could lead to passenger or crew discomfort in injury or, in the worst case, a flight safety critical situation. Depending on the particular aircraft type and age, maintenance costs can account for up to 20% of an airline’s operating costs, estimated to be at US$ 40 billion per year and worldwide [1]. Therefore, the most important question is how to reduce costs while assuring or improving safety and quality. One approach to this

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Chapter 1 - Aircraft systems reliability and safety enhancement via modelling and simulation

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problem is to optimise the applied maintenance strategy. Modern aircraft are designed to be fault-tolerant. The maintenance systems typically provide diagnosis of existing faults, but no information about the real-time remaining tolerance margin knowing the existing faults.

Figure 1.1 illustrates the classification of maintenance strategies with respect to the degree of preventive action ("act before failure") and their impact on costs. On the x-axis, the degree of preventive maintenance actions as part of all activities is shown, and on the y-axis are represented the costs.

Figure 1.1 - Impact of maintenance strategies on costs [1].

If no preventive maintenance is carried out at all (left), it is assumed that maintenance still has to be performed, but on a corrective basis resulting from system or component failure. Since faults are, often, not expectable, most of the maintenance time is unscheduled, leading to increased efforts (e.g. ad-hoc troubleshooting) and operational interruptions (e.g. flight delays) and relevant breakdown costs. Thus, the qualitative curve for repair and breakdown costs shows a decreasing behaviour for higher degrees of preventive actions. If all maintenance activities are preventive (right), it is assumed that almost no corrective actions apply, because most problems are fixed prior to any fault or failure. Then the applicable prevention costs are directly proportional to the frequency of actions, tending to infinity and thus showing

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uneconomical behaviour for the extreme case of preventing any corrective action. If both qualitative cost curves are added, the resulting qualitative relation shows an optimum in between the two strategies. Operating at this point is pursued by establishing intelligent maintenance. The concept either refers to the combination of the traditional two concepts (corrective maintenance and preventive maintenance) or the implementation of advanced maintenance strategies, such as predictive

maintenance.

1.2 Prognostics for maintenance enhancement

The word prognostics is originally a greek word “progignôskein” that means “to know in advance”. Prognosis can be defined as a forecast of the future course, a prediction of a situation. In engineering, the goal of a prognostic algorithms is to analyze sensor data from one or more flights (offline) and to predict the future health and condition of the components, up to estimate their Remaining Useful Life (RUL). Prognostics can thus make an evolution in maintenance and operation support, moving from “fail-and-fix” to “predict-and-prevent” strategy.

The use of prognostics can enable:

 Condition-based maintenance strategies, instead of time-based maintenance;  Optimal maintenance scheduling;

 Optimal spare parts purchase;

 Prolonging component life (by modifying the component operation/duty cycle);  Dormant failures prevention.

As prognostics is a process of prediction about the development of the damage phenomenom, it can be used only to predict faults caused by progressive degradations, like wear mechanisms, of which is possible to forecast the evolution (it can’t be used, instead, with sudden faults, like, for example, the electrical ones).

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The concept of prediction implies the system monitoring and evaluates health-state in order to derive information for decision making, whether any maintenance action shall be taken (diagnosis), as well as scheduling when an action shall be initiated (prognosis). It aims to overcome the disadvantages of the traditional maintenance concepts: it is expected to improve the planning of today’s correctively treated ad-hoc failures and thus to reduce the breakdown consequences. Whereas diagnostics still rely on the detection and identification of faults after these are occurred, the prognostic determination of the remaining useful life (RUL) allows to plan ahead before critical fault states occur [2].

Figure 1.2 - Benefits of diagnostics and prognostics [2].

The Figure 1.2 shows the benefits of the combined use of diagnosis and prognosis, in terms of cost and safety enhancement. Without prognosis we could have a service limit that is far from the real life consumption of the component or system, with consequently safety risks if the usage is more sever than expected or waste of useful life for milder usage, that would mean unnecessary maintenance activity and greater costs.

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1.2.1 Prognostics health management (PHM)

Prognostics is useful because it supplies the decision maker with early warning about the expected time to system failure and let him decide about appropriate actions to deal with this failure. The benefits from prognostics can be used for system health management [2]. System health management is a form of system diagnosis, in which the goal is to detect system failure and identify which component is responsible for it. In monitoring, the diagnosis is based only on observations derived from signals originating from sensors (e.g. pressure sensors or valve position detectors), it does not take into account the symptoms of failure (e.g. abnormal sounds or vibrations) or measurements performed by means of external devices (such as portable testers, which are often used during troubleshooting of the aircraft systems in repair shops). Health monitoring has the advantage of providing real-time health status either during the flight and/or soon after its completion.

PHM process combines the fault detection, isolation and identification given by system monitoring (diagnostics), with the process of prediction of faults, given by prognostics, so it can improve safety and reduce maintenance cost. PHM can also change the strategy in the system design and development by achieving high system reliability without adding many redundant devices. High reliability is achieved by replacing static reliability of the system calculated in design phase by online dynamic reliability calculation in actual operating conditions. The main objective of creating the PHM system is to to achieve, by combining different maintenance strategies (e.g., scheduled maintenance, condition-based maintenance, and predictive maintenance), optimum cost-effectiveness versus performance decisions. The ultimate goal regarding scheduled maintenance is a complete performance monitoring with a warning from the PHM system when the performance drops below a certain threshold (see Figure 1.3). This way, scheduled checks can be reduced to a minimum and unscheduled events become predictable.

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Figure 1.3 - Escalation of scheduled maintenance tasks. [1]

1.2.2 Prognostic approaches

Prognostic approaches can be classified in two categories, Figure 1.4:  Data-driven PHM;

 Model-based PHM;

Figure 1.4 Classification of prognostic approaches. [1]

The data-driven approach aims at creating a model that correlates the variation of some measured data of the system (e.g. pressure, temperature, speed) to system degradation and damage progression up to provide a RUL estimation [1]. The creation

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of this model is based on techniques from soft computing and sometimes techniques from statistics. The key requirement for data-driven prognostics algorithm development is the availability of multivariate historical data about system behavior, that must cover all phases of system normal and faulty operation as well as degradation scenarios under certain operating condition. The advantages are that no system knowledge is required and it is fast and easy to implement. The disvantages are: unavailability of data, specially for newly developed systems, and high computational effort, due to large datasets that affect the real-time performance.

In the model-based approach, a physical model for the system or component is developed [1]. This physical model is a mathematical representation of failure modes and degradation phenomena, that requires a thorough understanding of the system physics. In addition, knowledge about operating conditions and life cycle loads applied to the system are required. This methodology is very efficient and descriptive, it is often accurate, but accuracy and precision depend on model fidelity. The advantages of this approach are that it is easy to validate, certificate, and verify. There are some drawbacks and limitations of this approach such as: developing a high fidelity model for RUL estimation is very costly, time consuming, and computationally intensive and sometimes it could not be obtained. Also, if this expensive model is obtained, it will be component/system specific and its reusability will be very limited to other similar cases. For all of these reasons, sometimes the data-driven approach is used instead of the model-based one.

It could be a good solution to combine both model-based and data-driven methodologies into one hybrid approach to gain the benefits from each and overcome its limitation. Model-based can compensate the lack of data and data-driven compensates the lack of knowledge about system physics.

The complexity, cost, and accuracy of prognostics techniques is inversely proportional to its applicability. Increasing prognostics algorithm accuracy with low cost and complexity is a big challenge.

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1.3 Small Air Transport and More Electric Aircrafts

SAT (Small Air Transport) initiative represents the recent research and technology interest in small aircrafts used for carrying up to 19 passengers or for freight transport. The aim is to develop, validate and integrate key technologies in order to revitalize an important segment of the aeronautics sector that can bring key new mobility solutions [3].

Figure 1.5 – SAT [3].

Europe has adopted the Flightpath 2050 challenge: that by 2050, 90% of the population will be able to reach any location in Europe within four hours. Without the Small Air Transport System, which can be optimized for short distances and for multiple but thin passenger flows, this challenge cannot be met. SAT aircraft have the agility to take off and land in tiny regional or even remote utility airports, are frugal when it comes to fuel consumption, have fast turnaround times, and can be deployed on routes that would not be geographically or economically viable by rail or road nor by their larger brethren such as regional turboprops or jets. Small Air Transport fulfills a market segment that cannot be filled by other types of aircraft, nor can it be

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addressed by other modes of transport. This provides route agility that is increasingly important in a fast-changing European landscape [4] [5].

This new transport system will increase the number of aircrafts and flights, involving a major number of pilots and major risks. This means safer and more efficient small aircraft operations are required. The way to do that is automation, allowing situation awareness and single pilot operations. The technology should assist piloting, requiring less trained pilots and increasing safety. Innovative take-off and landing techniques are also required. The aim, in the long term, is to reach a level of automation that will lead to fully automated SAT aircraft flying, according to autonomous flight rules. Concurrently to this aim for the future to reach a new type of air transport dominated by small and more automated aircrafts, we have to consider the tendency of the recent years to increment the use of electric power onboard, a trend that takes the name of More-Electric Aircraft (MEA) and will soon lead to All-Electric Aircraft (AEA). The all-electric aircraft (AEA) refers to an aircraft fully powered by electricity and where no fuel is involved. In an all-electric aircraft, the propulsion, onboard equipments and instruments are all powered electrically by electrical storage or electrical generation systems. Electrical system, compared to equivalent hydraulic ones, shows high gains in safety, reconfiguration and maintenance, besides a minor impact to the environment. The use of all electric strategy removes the problems related to hydraulic and pneumatic system, like issues of size, shape and location of aerodynamic surface and system layout. Integration is easier too, because the designers are dealing with only one type of technology. An additional benefit is the increased mission adaptability, because digital flight control systems are driven by software, changes in the control system performance are easier to realize than with conventional mechanical systems, making possible to change the control laws depending on the particular mission. [6]

The benefits using all-electric aircraft can be summarized as follows:  Reduction of costs;

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 Simpler maintenance.

1.3.1 Electro-mechanical actuation systems

In order to pursue the concept of MEA, new solutions have been developed to replace hydraulic equipments by electro mechanical activation systems. For example, the current trend is to use the technology named EMAs (Electro-Mechanical Actuator) for the movement of the nose wheel steering, instead of the consolidated hydraulic actuator.The nose wheel steering system is thus an electromechanical rotary actuator electrically supplied and controlled in closed loop by an electronic control unit. One of the main problems of using electro-mechanical actuators is that this is an early technology, for in flight use, not yet consolidated and there are not much statistical database regarding their fault modes. So, these actuators become safety-critical components and an unidentified fault inside of them could lead to serious safety problems [7].

1.3.2 Stand-by systems

To make up for the lack of knowledge of reliability, with which aircraft innovations are always accompanied, an effective solution is to insert beside the new device a stand-by system that can supply the principal system functions in case of failure of this last one. For example, in the case of electro-mechanical actuators implemented in light jets instead of the hydraulic actuator for the motion of the nose steering, a stand-by

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system for the lateral directional control is represented by the differential brakes that activate when a failure occurs to the steering actuator.

All these motivations lead us to use, as case study for our purpose, a light jet aircraft with electro-mechanical steering actuator and differential brakes in active/stand-by configuration.

1.4 Landing roll-out simulator

The studies carried on in this thesis refer to a landing roll-out flight simulator of a light jet aircraft developed in previous thesis works.

This model includes the 6-DOFs dynamics of the aircraft (with the hypothesis of: rigid body, constant mass, negligible gyroscopic effects of rotating masses, symmetric thrust and negligible structural deformations) and detailed models of hydraulic brakes, shock-absorbers, tire loads (the Dugoff model evaluates the interaction forces between tire and runway [8]). The directional control system is based on a nested architecture of the four closed loop controls for the directional control of the aircraft, through the combined use of standard commands, steering and rudder, and hydraulic differential brakes [9]. The work was focused on the design and verification of the aircraft simulator control laws, with particular reference to brake pressure control, heading control and ground path control [10].

A transfer function of the nose wheel steering actuator has been received from a parallel activity about the control of an electro-mechanic actuator [7].

A model of main landing gears with a tripod-type configuration and variable wheel track has been integrated in the aircraft simulator, demonstrating that it increases the directional control capabilities of differential brakes. It has also been introduce a new anti-skid control that includes gear walk suppression capabilities in order to prevent instability of main landing gear vibration during the braking phase [11].

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Basic architecture of the directional control laws

Figure 1.6 - Basic architecture of the directional control laws.

The basic concept for the directional control laws is that rudder, nose wheel steering and differential brakes simultaneously work to align the aircraft to the demanded runway path, while the vehicle is decelerating. A scheme of the nested loops is depicted in Figure 1.6. The model has many closed loop, listed from the innermost one to the most external one:

o brakes pressure control; o anti-skid & heading control o ground path control

The pressure loop has to follow the requested pressure coming from the block Antiskid and Heading regulators. The anti-skid loop has to permit a good rolling of the wheel without any blocking of the tire; the heading loop, through the three command axes, has the task to realign the aircraft on the center line of the runway. The ground path loop gives the right signal to the heading loop to reduce the distance to the center line. The pourpose is to reduce lateral gap and longitudinal path maintaining the safety margins requested by flying qualities.

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1.3.1 Reference aircraft

The reference aircraft is a business jet aircraft with a T-tail [12]. The geometric features are depicted in Figure 1.7 and Table 1.1.

Figure 1.7 – Reference aircraft details [12].

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1.3.2 Antiskid differential brakes system

The high ground speeds that are recorded during the landing phase right after the tocuhdown and the need to stop the aircraft within the available runway distance, lead to high wheel braking forces generated on the tire. Since a relatively short duration of tire skid at high speed may result in a loss of directional control, or even cause a tire blowout with consequently severe damages, experience has established that a wheel brake antiskid feature is required for safe aircraft operation.

Anti-skid systems are designed to minimize aquaplaning and the potential tire damage which can occur when a wheel is locked or rotating at a speed which does not correspond to the speed of the aircraft, also greatly improves stopping distance on substandard surfaces such as gravel or grass and is particularly effective on surfaces with frozen contaminants such as ice or slush by ensuring maximum effective breaking. The anti-skid system compares the translational ground velocity of the aircraft with the tangential rotational velocity of the wheel: if this one is lower than the aircraft speed, the brake on the wheel is released momentarily to allow the wheel to regain speed and prevent the wheel from skidding.

Figure 1.8 - The development of a skid by on-and-off brake application [13]. In Figure 1.8, we can see how the antiskid works. When the brakes are applied, the pressure rises until the wheel starts to slip, but not skid (point A). This is the ideal

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condition, but the pilot has no indication that it has been reached, so he continues to increase the force on the brake pedal. A pressure is soon reached which produces enough friction in the brake to cause the tire to start to skid on the runway (point B). The wheel now decelerates fast enough that the pilot can feel it, so he releases the pedal. But since the braking force required becomes less as the wheel slows down the wheel continues to decelerate even though the brake pressure is decreasing. At point C, the wheel has completely locked up, and the pressure is still dropping. At point D, the pressure is low enough for the friction between the tire and the runway surface to start the wheel rotating again, and soon after the brake pressure drops to zero, the wheel has come back up to speed. [13]

The system is fully automated and his system components usually consist of: wheel speed sensing units, antiskid control elements and antiskid brake torque control valves.

In the Figure 1.9 is indicate the antiskid loop in the simulator, that takes as input the desired symmetrical slip ratio plus the differential contribute and return as output the angular velocity of the wheels.

Figure 1.9 – Antiskid closed loop.

The antiskid is essential for the correct action of the differential brakes, both for what concern the stopping of the aircraft and the lateral control of it during the landing roll-out.

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Figure 1.10 illustrates how rudder, differential brakes and nose wheel steering influence the directional control capability of the aircraft as function of the ground speed from touchdown to a full stop. We can notice how without an appropriate antiskid control the differential brakes contribute at high speeds is null, as a blockage of the wheels at that speeds would make ineffective the action of the command, as well as being a risk for the safety. The yellow area is the “gain” in control capability that we have with a proper antiskid control.

Figure 1.10 - Influence of nose steering, differential brakes and rudder on ground directional control.

1.5 Landing roll-out: a critical mission phase

Landing is the most critical phase in a typical civil aircraft mission. In fact, as reported in the Statistical Summary of Commercial Jet Airplane Accidents in Worldwide

Operations, published by Boeing [14], the landing phase, wich is only 1% of the total

flight duration, has a high percentage of fatal accidents (24%), Figure 1.11.

In particular, in Figure 1.12 the main reasons of onboard fatalities are shown and third principal reason is actually the “Runway Excursion”.

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A runway excursion is the event in which an aircraft veers off or overruns the runway surface during either takeoff or landing. Landing overruns and veeroffs are the most common type of runway excursion accounting for more than 77% of all excursions. There are at least two runway excursions each week worldwide. Runway excursions can result in loss of life and/or damage to aircraft, buildings or other items struck by the aircraft. A statistical analysis of most important causal factors in landing veer offs is shown in Figure 1.13. [15]

Figure 1.13 - Most important causal factors for landing veer offs. [15]

Wet/contaminated runways and crosswind appear to be dominating causal factors. Crosswinds exceeding the capabilities of the aircraft or inadequate compensation by the pilots (see the factor Aircraft directional control not maintained in Figure 1.13) are the reasons for the influence of this factor. In 36% of the landing veeroffs in which crosswind was cited as a causal factor, the runway was also wet/contaminated. Furthermore, the risk of a landing overrun is about 13 times higher on a wet/contaminated runway than on a dry runway (wet/contamined runway represent the 58.8% of the causes of landing overruns). In this perspective, it assumes a great importance the development of automatic systems for the directional control of the aircraft during the ground portion of the landing procedure.

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Another important factor in landing veeroffs is nose wheel steering issues, which main reasons are improper maintenance and incorrect use of the steering system. Here the importance to study a configuration where the failure of the steering is compensated by a stand-by control command, like the differential brakes.

Eventually we can see how also tire failure is another important cause in landing veer offs, usually related to a hard landing or a consequence of a nose wheel steering failure, that cause the tire to skid above the normal limits allowed by the anti-skid control, with high risks for the safety.

Hence the importance to study the landing roll-out phase and improve the aircraft capabilities in this portion of the mission, with specifically attention to the nose steering failure condition and the tires health-management.

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Chapter 2

Tire loads modelling

In the aeronautics transport domain, the improvement of the security, the reliability and the comfort requires also a reliable control of the aircraft on the ground. Since the tire is the only contact point of the aircraft with the ground, the tire properties would play a fundamental role when determining the aircraft dynamic behaviour. Thus advanced and representative tire model is necessary.

2.1 Tire loads

The dominant factor influencing the operation of an antiskid brake control system is the characteristic behavior of a rolling tire while being subjected to braking forces. This behavior is shown on Figure 2.1:

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Chapter 2- Tire loads modelling

22

As a small braking force is applied, an apparent slippage develops between the tire and the contacting surface. This apparent slippage is evidenced by the wheel angular velocity being less than the synchronous angular velocity, that results from unbraked rolling, by an amount proportional to the the braking force. The initial apparent slippage occurs without appreciable relative motion between the tire footprint and contacting surface, because of elastic deformations within the tire. This correspond to the stable condition (region A in the figure 2.1) where there is a positive-slope portion of the relationship. If an increase in the applied braking torque to a value exceeding the available friction torque is attempted, an actual slippage between the tire and the surface results, tire slippage will increase into the negative-slope region of the brake force (region B in Figure 2.1. This results in an unstable ever increasing negative wheel angular acceleration, where the friction coefficient decreases as sliding velocity increases. A full skid will result if the brake torque is not quickly reduced to some value less than the instantaneous friction torque so that a positive wheel angular acceleration is produced causing the wheel to regain speed. When the apparent wheel slippage reaches the 100%, the angular velocity of the wheel is zero, the wheel is completely blocked and it slips over the runway at the same velocity of the plane. [18] In order to better describe this behaviour, we use a parameter that relates the apparent slippage of the wheel to the forward speed of the aircraft, the Slip Ratio.

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In according with the nomenclature shown in Figure 2.2 , the slip ratio of the wheel is defined as follows:

= ̇ − ̇

̇

(2.1) where ̇ is the axle transational velocity, ̇ is the wheel angular velocity and is the tire unbraked apparent rolling radius; ( ̇ − ̇ ) is thus the apparent wheel slippage.

Besides the Slip Ratio, another coefficient is used to describe the behaiour of the tire: the Slip Angle. The slip angle (α) is defined as the angle between the wheel velocity vector and the wheel itself orientation direction. When a steering command (δ) is given, or either in the case of surface with differents friction coefficients, in addition to the longitudinal friction force, it generates a lateral friction force, in the same direction of the wheel angular velocity, proportional to the slip angle (α). The Slip Angle is thus an indication of the amount of this lateral friction force generated; when α is zero, ther is no lateral force (for example in the case of symmetrical braking).

Figure 2.3 - Slip Angle.

For the nose steering wheel the slip angle is defined as follows (in according to figure 2.3):

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Chapter 2- Tire loads modelling 24 = − (2.2) = + ̇ (2.3) where and are the components of the wheel velocity in the body axes, ̇ is the yaw angular velocity of the plane and is the distance between the nose steering gear and the center of gravity of the plane.

For the main gear wheels the slip angle is definde as:

= − (2.4)

= − ̇

(2.5) where , and ̇ are defined as above and is the distance between the main gear and center of gravity of the plane.

In Figures 2.4 and 2.5 are represented the curves of the longitudinal and lateral friction coefficients in function of the slip ratio and slip angle.

Figure 2.4 – Longitudinal and lateral friction coefficients in function of the slip ratio with increasing slip angle [18].

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We can see how this curves highly depend on the runway conditions (dry or wet) and also on the combined action of both lateral and longitudinal forces that are generated in the interaction with the runway.

Figure 2.5 - Longitudinal and lateral friction coefficients in function of the slip ratio and slip angle for wet and dry runway condition [18].

In fact, as shown in Figure 2.4, as the slip angle increases the longitudinal friction coefficient decreases and his maximum value shifts to higher slip ratio values. On the other side, the lateral friction coefficient increases as the slip angle increases and the highest values are for low slip ratio values. The antiskid system must then be able to accomplish tasks with very different goals. In example, considering the case of landing with lateral wind on wet runway: it would desiderable a high slip ratio in order to have a high longitudinal braking force that reduces the stopping path; on the other hand it has to be granted low values of the slip ratio to assure the directional control of the aircraft.

There are many models that describe the non linear behaviour of the tire, such as:  Physical Models, the expressions of the tire characteristics are developed

based on tire displacement in the contact patch, which depends on its physical properties [17];

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 Semi-Empirical Models, based on observed data and also contain structures that find their origin in physical models [17];

 Empirical Models, based only on observed data [17].

So far, the model that has been utilized, for the main gear as for the nose gear, is the semi-empirical model of Dugoff. The aim is to improve the funcionalities of the simulator introducing a tire model that is closer to the real behaviour of the tire.

2.2 Comparison of tire models

In the previous thesis the model used to describe the behaviour of the tires in the interaction with the runway is the Dugoff model. As shown in the Figure 2.6, this model gives longitudinal forces (in the grapich it has been preferred to represent the adimensional longitudinal friction coefficient µ = ) that diverge from the experimental data (found in literature). In particular, it occours in the peak area that is not at all represented by the Dugoff results. Clearly, the implementation of a model in the simulator that is far from the real behaviour could cause instability problems. The empirical Pacejka model, otherwise, provides simulation results that better fit measurements data, for what concern the longitudinal forces. Analizing the graph of lateral friction coefficient we can see how the Pacejka model doesn’t follow the trend of the experimental data. This isn’t an issue when modelling the behaviour of the main gear’s tires, as the main forces here, wich we are interested to know with accuracy, are the longitudinal ones.

The same is not valid when we analyze the nose gear forces, for these are mostly entirely lateral forces. The Pacejka model is then not appropriate, so we use a “Magic Formula” that has been studied expressly to calculate the cornering force of the nose gear for that type of aircraft [7].

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2.1 Tire models in the flight simulator

As said before, in order to improve the capabilites of the simulator, we have implemented tire models that are closer to the real behaviour, that means the Pacejka Model for the main gear and the Magic Formula for the nose gear. We have then done a simulation in both dry and wet runway condition to compare the results with the ones obtained with the previous model.

Main Gear

For the main gear, the longitudinal (Fx) and lateral (Fy) forces are calculated using the

Pacejka model [18]. The equations given by Pacejka are:

( ) = [ ∙ ( − ( − arctan ( )))] (2.6) ( ) = ( ) + (2.7) = + (2.8) Where:

Y: Model Output (Fx or Fy);

X: Model Input Variable (α or λ); B: Stiffness Factor; C: Shape Factor; D: Peak Value; E: Curvature Factor; Sh: Horizontal Shift; Sv: Vertical Shift;

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29 The asymptotic value is given by: =

Figure 2.7 illustrates an example of a shear force representation by Pacejka’s formula, where ys is the asymptotic value at large slip values, and xm the input variable at which

the shear force reaches its peak value D.

Figure 2.7- Example, force representation by Pacejka’s Formula.

In the Table 2.1 are summarized the coefficients that have been used in the simulations to estimate the Pacejka curves, both longitudinal and lateral, for dry and wet runway condition. The horizontal and vertical shift are setted to zero because we do not take in account the camber of the tire, that can be neglected for the purposal of this simulation. [19]

In the figures 2.8 and 2.9 the longitudinal friction coefficients calculated with the current model of Pacejka are compared, with the results given by the previous simulator employing Dugoff model. The comparison is done for dry and wet runway. We can notice how the initial slope and the asymptotic value at Slip Ratio=1 are the same for both curves.

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X

Coeff.

λ

α

Dry Wet Dry Wet

B 6.5 10.5 10.3 12.4 C 1.346 1.323 1.324 1.312 D 0.86 0.43 0.457 0.229 E -4 -1.2 -1.347 0.126 Sh 0 0 0 0 Sv 0 0 0 0 ys 0.736 0.376 0.399 0.202

Table 2.1 – Coefficients of Pacejka Model.

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Figure 2.9 - Comparison between Dugoff Model and Pacejka Model, wet runway.

Nose gear

For what concern the nose gear, the cornering force generated by the tire is calculate using the Magic Formula utilised in [7].

The cornering force trend can be approximated by a hyperbolic tangent trend:

( , ) = µ ℎ

( )

(2.9) It is thus defined the lateral coefficient as the derivative of the cornering force with respect to the slip angle.

( ) =

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In order to calculate the lateral coefficient, Skynetics provides a magic formula:

( ) = −

(2.11) With magic formula parameters:

 p = −5.614;  p = 0.909;  p = 2.5;  F = 8251 N;

Combining the two equations above it is possible to calculate the function .

( ) = = µ

( ) 1 − ℎ ( ) =

µ ( )

(2.12) Where µ = 0.8 is the lateral friction coefficient

So:

( ) = µ ( )

(2.13) In the Figures 2.10 and 2.11 the lateral friction coefficients calculated with the current magic formula model are compared, with the results given by the previous simulator employing Dugoff model. The comparison is done for dry and wet runway. We can notice how the initial slope and the asymptotic value at Slip Ratio=1 are the same for both curves.

In Figures 2.12 and 2.13 the results of longitudinal velocity of the aircraft, in dry and wet runway condition, obtained with the previous and current tire model simulations, are compared.

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Figure 2.10 – Comparison between Dugoff Model and Magic Formula for the nose steering, dry runway.

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Figure 2.12 – Comparison of aircraft velocity, dry runway.

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Chapter 3

Failure transients analysis for the

fault-tolerant directional control system

The goal of this part of the work is to verify and compare the lateral control capabilities of the various command axes, with special attention to the steering and the differential brakes, in view of the particular aircraft configuration active/stand-by steering and differential brakes. A closer analysis of this configuration is done, afterwards, testing the simulator to respond at a steering failure, with a specific attention to the transients’ behaviour, identifying the requirements for a safe and performing directional control.

3.1 Test campaign definition

Generally, the events that happen during a landing are:

 touchdown: the aircraft touches the runway for the first time;

 the shock absorbers feel the weight and respond with a vertical dynamic;  the propulsion is decreased and shut-off;

 after few seconds the brake system is activated;

 the aircraft decelerates (by responding on all axes of motion to disturbances).

In the simulations, these events are considered with the following parameters and initial conditions:

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Chapter 3- Failure transients in fault-tolerant directional system

36

 = 2.5 s, time when the brakes are activated;

 = 3s, time when the gust runs over the aircraft;

 = 50m/s, initial velocity of the aircraft;

 = 0 rad/s, initial angular velocity of the wheels;  μ = 0.8, dry runway friction coefficient;

 μ = 0.4, wet runway friction coefficient;

 = 1 m/s, stop simulation velocity (taxi speed);

 = 0.05, slip ratio parameter.

Initially the shock absorber is completely extended and the other variables, that are not mentioned, are set to zero.

3.2 Commands and disturbances time histories

Thrust

The thrust of both engines has an initial constant value that balances the aircraft’s drag. At time 2.5 seconds, the thrust decay to zero within a second, like − / .

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Bump Gusts

The shape of the bump gust is modelled according to [20]:

= 0 ≤ 0 2 1 − cos 2 25 ̅ 0 < < 75 ̅ 0 ≥ 75 ̅ (3.1) where:

 s is the distance penetrated into gust and is given by = ∫ and = 3 ;

 is the mean geometric chord of wing;  (50 ft/s) is the derived gust velocity.

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Constant Gust

A more severe gust is taken in account: it raises like 1-cos and stays on the maximum constant value until the end of the landing manouvre.

= ⎩ ⎪ ⎨ ⎪ ⎧ 0 ≤ 0 2 1 − cos 2 25 ̅ 0 < < 75 2 ̅ 2 ≥ 75 2 ̅ (3.2)

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Failure injection + latency

At a certain instant ( ) we introduce a failure of the steering, so the boolean variable passes from one (active steering) to zero (failure condition, blocked steering) and after a time of latency ( ) the differential brakes are activated, its boolean switching from zero (inactive differential brakes) to one (active differential brakes).

Figure 3.4 – Failure injection and time of latency.

In the Figure 3.5 is depicted the external closed loop and relative blocks of the flight simulator, developed in Simulink.

The integration method used in the simulations is Runge-Kutta and the integration step is equal to 10e−4_.

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3.3 Command axis authority

With the intent of knowing the authority of the various command axis, in other words the exploit of each of them in reference to their maximum capabilites, we have defined the Yaw Moment-Aircraft Velocity Graph, where the yaw moment generated by each command is represented for different weather conditions (bump gust or costant gust combined with wet or dry runway), in function of the longitudinal aircraft velocity, togheter with their maximum values.

Maximum Yaw Moment

For the evaluation of the maximum moments we consider the limit conditions for each command. For all of them we use the maximum value of the friction coefficient:

= 0,8 o Differential Brakes:

we consider a wheel completely blocked and the other in free rolling, the nominal static value of the vertical load and the maximum wheel track;

= 18909

= 1,255 + 0,35 = 1,605

The moment is given by the frictional force generated by the tire, multiplied by distance between one wheel and the center of gravity of the aircraft , so:

=

that results in an horizontal straight line. o Steering:

we consider the steering blocked, with the nominal static value of the vertical load on the nose wheel;

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= 6679 = 4,19

The moment is given by the frictional force generated by nose tire, multiplied by the distance of the nose gear from the center of gravity of the aircraft, so:

=

that results in an horizontal straight line. o Rudder:

we consider the rudder blocked at the maximum angle; = 10

= 4,72 = 0,1574

= 10,4

The moment is given by the aerodynamic force generated by the rudder, multiplied by the distance between this last one and the center of gravity of the aircraft, so:

=1

2

that results in a parabola.

In the following figures, the yaw moment graphs resulting from the simulations with all three command axes activated are depicted, for bump gust and costant gust on dry and wet runway . (All the moments are represented in their absolute value for a better display of the results).

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Figure 3.6- Yaw Moments, Bump gust & Dry runway.

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Figure 3.8- Yaw Moments, Bump gust & Wet runway.

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3.4 Comparison of single command performances

In order to have a better comprehension of how each command axis concur to the directional control of the aircraft and in wich measure, a series of simulations is done at differents runway conditions and for both types of gust (bump and constant), so that we can compare the performance of the rudder, the steering and the differential brakes alone. The Table 3.1 summarises the results obtained in these simulations of the meaning parameters that better represent the performances of the aircraft, those are:

 max , the maximum yaw angle considered as absolute value (as the gust is

positive all the yaw angles shown in the table are negative);

 the maximum lateral displacement of the aircraft’s center of gravity from the center line of the runway;

 the path, that is the total longitudinal distance that takes the aircraft to stop;

 the time of simulation.

As the results of the only rudder simulations diverge, we have set the time simulation to 20 seconds in order to obtain results that are comparable with the ones of the other command axis simulations.

Moreover, in the Figures from 3.10 to 3.17 (view also Appendix A) are represented the aircarft’s center of gravity trajectory (the dotted lines symbolise the passageway in which the aircraft has to be to satisfy the requirements of the flying qualities) and the yaw moments in function of the aircraft velocity, for the various simulations. It worths notice that in the simulations with the command axis of the differential brakes setted off, there is still a yaw moment generated by the brakes themselves. However this is a passive contribution to the yaw moment, that means that in some cases it can help the other commands in the directional control of the aircraft, but in other cases it countreact their action, aggravating the loss of lateral direction control.

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Dry Runway & Constant Gust

Rudder

Figure 3.10 - Aircraft trajectory, only Rudder. Dry Runway and Constant Gust.

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47 Steering

Figure 3.12 – Aircraft trajectory, only steering. Dry Runway and Constant Gust.

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Differential Brakes

Figure 3.14- Aircraft trajectory, Differential Brakes. Dry Runway and Constant Gust.

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Steering + Differential Brakes

Figure 3.16 - Aircraft trajectory, Steering and Differential Brakes. Dry Runway and Constant Gust.

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Summary of results

max [deg] Max lateral

displacement [m]

Path [m] Time [s]

Dry Runway and Bump Gust

Rudder 1.59 0.64 738 20

Steering 0.96 0.39 739 39

Differential Brakes 0.81 0.37 738 39

S+DB 0.74 0.33 737 39

S+DB+R 0.73 0.32 737 39

Dry Runway and Constant Gust

Rudder 1.84 1.04 826 20

Steering 1.46 0.93 848 45

S+DB 1.21 0.77 826 45

Wet Runway and Bump Gust

Steering 1.59 0.68 840 43

Wet Runway and Constant Gust

Steering 3.40 2.18 994 50

Table 3.1 Single command axis simulation results.

The first result that emerge from the simulations is that the rudder only is not capable of control direction. In fact, as we can see in Figure 3.10, the aircraft exceeds the runway lateral limits in the case of dry runway and constant gust, besides that already in the less severe condition of bump gust the directional control is not effective as with the other two commands; the reason can be easy found in the fact that the aircraft,

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during the landing and the roll-out phase, is decelerating, so as the velocity decreases, the rudder is no longer able to generate a lateral force that would permit the directional control. In addition, comparing the simulation with all the three axes active and the one without the rudder, results that the rudder has very little influence in relation to the steering and differential brakes action, so it can be neglected: in other words the rudder command can be turned off once the aircraft touches the ground. For what concern the two commands remaining, that are the steering and the differential brakes, we can evince from the results of the simulations that they are equivalent regarding the directional control capability; in fact, in all the simulation conditions, the path, maximum yaw angle and maximum lateral displacement are comparable for both commands. We can also see, from Figure 3.16, that using both steering and differential brakes at the same time doesn’t improve the performances in a considerable way, therefore is more convenient to use only one of them at a time.

Differrential Brakes alone configuration

As seen before, the differential brakes command alone satisfies the directional control requirements. We can so think of a possible application where the differential brakes accomplish the lateral control task and the steering command disappears, leaving the front gear free to rotate as the plane changes his direction on the runway. This results into remove the steering actuator, which means minor weight, so minor costs. On the other hand, we would face a lack of reliability using only the differential brakes, for this reason this solution is not applicable in the civil air transport. Neverthless, this configuration could find some use in the development of drone technology, where the requirements of reliability are less severe and the need of reduction of weight is a priority.