The Pennsylvania State University

The Graduate School

College of Engineering

DAMAGE MITIGATION FOR ROTORCRAFT THROUGH LOAD

ALLEVIATING CONTROL

A Thesis in

Aerospace Engineering

by

David B. Caudle

c 2014 David B. Caudle

Submitted in Partial Fulfillment

of the Requirements

for the Degree of

Master of Science

December 2014 The thesis of David B. Caudle was reviewed and approved∗ by the following:

Joseph F. Horn Professor of Aerospace Engineering Thesis Advisor

Asok Ray Distinguished Professor of Mechanical Engineering, Electrical Engineering, Mathematics

and Nuclear Engineering

George A. Lesieutre Professor of Aerospace Engineering Head of the Department of Aerospace Engineering

∗Signatures are on file in the Graduate School.

ii Abstract

A control method was developed to reduce the fatigue damage caused to critical rotorcraft hub components. This control method was demonstrated using simulation models of a utility heli- copter similar to a UH-60 Black Hawk and a large heavy-lift transport helicopter similar to a

CH-53E Super Stallion. The components of interest were the pitch link, rotor shaft, and the stationary scissors. The component loads were related to vehicle states and limited within the control system. Batch and piloted simulations were conducted in the Penn State Flight Simula- tion Facility for both vehicles to evaluate the effectiveness of the damage mitigation control. The fatigue damage experienced by the critical components was shown to decrease during aggressive maneuvers at high airspeeds. Furthermore, implementing this control system caused only a slight degradation to the handling qualities.

iii Table of Contents

List of Figures vi

List of Tables ix

List of Symbols x

Acknowledgments xiii

Chapter 1 Introduction 1 1.1 Motivation ...... 1 1.2 Background ...... 2 1.3 Research Objective and Thesis Organization ...... 5

Chapter 2 Model Development 7 2.1 FLIGHTLAB Software ...... 7 2.2 Utility Helicopter Development ...... 8 2.2.1 Rigid Blade Model ...... 8 2.2.2 Flexible Blade Model ...... 9 2.2.3 Response Characteristics ...... 10 2.3 Heavy-Lift Transport Helicopter Development ...... 21 2.3.1 Flight Model ...... 21 2.3.2 Open Loop Control ...... 25 2.3.3 Model Verification and Response Characteristics ...... 25

Chapter 3 Controller Design 31 3.1 Dynamic Inversion Control Law ...... 31 3.2 Implementation and Response Type ...... 33 3.3 Load Limiting Control and Logic ...... 35 3.3.1 Utility Helicopter Limits ...... 35 3.3.2 Heavy-Lift Transport Helicopter Limits ...... 39

Chapter 4 Damage Model 41 4.1 Utility Helicopter ...... 41

iv 4.1.1 Fatigue Crack Growth Model ...... 42 4.1.2 Component Loads and Structural Model ...... 43 4.2 Heavy-Lift Transport Helicopter Damage Model ...... 44

Chapter 5 Simulation and Evaluation 45 5.1 Simulation Environment ...... 45 5.1.1 Simulator Hardware ...... 45 5.1.2 Simulator Software ...... 46 5.2 Simulation Method ...... 47 5.3 Utility Helicopter Simulation ...... 48 5.3.1 Loads and Damage Reduction ...... 48 5.3.1.1 Batch Simulations ...... 48 5.3.1.2 Piloted Simulations ...... 56 5.3.2 Handling Qualities ...... 66 5.4 Heavy-Lift Transport Helicopter Simulation ...... 70 5.4.1 Loads and Damage Reduction ...... 70 5.4.1.1 Batch Simulations ...... 70 5.4.1.2 Piloted Simulations ...... 75 5.4.2 Handling Qualities ...... 80

Chapter 6 Conclusions and Future Work 82

Appendix CSGE Diagrams 84

References 92

v List of Figures

1.1 CH-53E Super Stallion (From Ref. [1]) ...... 2 1.2 UH-60 Black Hawk (From Ref. [2]) ...... 2 1.3 Articulated Rotor Hub Showing Pitch Links and Stationary Scissors (from Ref. [3]) 3

2.1 Pitch Rate to Longitudinal Stick Frequency Response at 60 knots for the Rigid Blade Utility Helicopter ...... 12 2.2 Roll Rate to Lateral Stick Frequency Response at 60 knots for the Rigid Blade Utility Helicopter ...... 12 2.3 Pitch Rate to Longitudinal Stick Frequency Response at 120 knots for the Rigid Blade Utility Helicopter ...... 13 2.4 Roll Rate to Lateral Stick Frequency Response at 120 knots for the Rigid Blade Utility Helicopter ...... 13 2.5 Pitch Rate to Longitudinal Stick Frequency Response at 60 knots for the Flexible Blade Utility Helicopter ...... 14 2.6 Roll Rate to Lateral Stick Frequency Response at 60 knots for the Flexible Blade Utility Helicopter ...... 14 2.7 Pitch Rate to Longitudinal Stick Frequency Response at 120 knots for the Flexible Blade Utility Helicopter ...... 15 2.8 Roll Rate to Lateral Stick Frequency Response at 120 knots for the Flexible Blade Utility Helicopter ...... 15 2.9 Roll Rate to Lateral Stick Comparison of Utility Helicopter to Test Data at 80 knots from Reference [22] ...... 16 2.10 Trimmed Stick Position Comparison for Rigid Blade and Flexible Blade Utility Helicopter Models ...... 17 2.11 Stick Input for Time Histories ...... 18 2.12 On-Axis Attitude Response Comparison of Rigid and Flexible Blade Models at 120 knots ...... 19 2.13 On-Axis Rate Response Comparison of Rigid and Flexible Blade Models at 120 knots ...... 20 2.14 Fuselage Incremental Rolling Moment as a Function of Angle of Attack . . . . . 22 2.15 Fuselage Incremental Rolling Moment as a Function of Sideslip (Wind Tunnel Yaw Angle) ...... 22 2.16 Fuselage Roll Moment as a Function of Angle of Attack and Sideslip ...... 23 2.17 Fuselage Incremental Lifting Force as a Function of Angle of Attack ...... 23 2.18 Fuselage Incremental Lifting Force as a Function of Sideslip (Wind Tunnel Yaw Angle) ...... 23 2.19 Fuselage Lift Force as a Function of Angle of Attack and Sideslip ...... 24

vi 2.20 Trimmed Pitch Attitude Comparison of FLIGHTLAB Model with NATOPS Report 26 2.21 Trimmed Torque Requirement Comparison of FLIGHTLAB Model with NATOPS Report ...... 26 2.22 Pitch Rate to Longitudinal Stick Frequency Response at 60 knots for the Heavy- Lift Transport Helicopter ...... 27 2.23 Roll Rate to Lateral Stick Frequency Response at 60 knots for the Heavy-Lift Transport Helicopter ...... 28 2.24 Pitch Rate to Longitudinal Stick Frequency Response at 120 knots for the Heavy- Lift Transport Helicopter ...... 28 2.25 Roll Rate to Lateral Stick Frequency Response at 120 knots for the Heavy-Lift Transport Helicopter ...... 29 2.26 Roll Rate to Lateral Stick Frequency Response Comparison Between the Heavy- Lift Transport Helicopter FLIGHTLAB Model and Test Data in Hover from Ref- erence [27] ...... 30 2.27 Roll Rate to Lateral Stick Frequency Response Comparison Between the Heavy- Lift Transport Helicopter FLIGHTLAB Model and Test Data at 70 knots from Reference [27] ...... 30

3.1 Dynamic Inversion Control Law Architecture ...... 33 3.2 Command Filter with Rate Limiter ...... 36 3.3 Pitch Link Load in Steady Level Flight at 120 knots ...... 37 3.4 Pitch Link Load During Aggressive Maneuver at 120 knots ...... 37 3.5 Load Factor Time History for Various Airspeeds ...... 38 3.6 Load Factor Limit Determination for Pitch Link Load at Various Airspeeds . . . 38 3.7 Roll Rate Limit Determination for Pitch Link Load at Various Airspeeds . . . . 39

5.1 Flight Simulator at The Pennsylvania State University ...... 46 5.2 Stick Inputs for the Batch Pitch Doublet Simulations ...... 48 5.3 Stick Inputs for the Batch Roll Doublet Simulations ...... 49 5.4 Utility Helicopter Attitude Response to Pitch Doublet Maneuver ...... 50 5.5 Utility Helicopter Rate Response to Pitch Doublet Maneuver ...... 51 5.6 Utility Helicopter Response to Pitch Doublet Maneuver ...... 52 5.7 Utility Helicopter Pitch Link Loads and Crack Growth for Pitch Doublet Maneuver 52 5.8 Utility Helicopter Crack Growth Over Pitch Link Lifetime from Repeated Pitch Doublet Maneuvers ...... 53 5.9 Utility Helicopter Attitude Response to Roll Doublet Maneuver ...... 54 5.10 Utility Helicopter Rate Response to Roll Doublet Maneuver ...... 55 5.11 Utility Helicopter Pitch Link Loads and Crack Growth for Roll Doublet Maneuver 55 5.12 Utility Helicopter Crack Growth Over Pitch Link Lifetime from Repeated Roll Doublet Maneuvers ...... 56 5.13 Utility Helicopter Stick Inputs for the Piloted Pitch Doublet Maneuver ...... 57 5.14 Utility Helicopter Attitudes for Piloted Pitch Doublet Maneuver ...... 58 5.15 Utility Helicopter Rates for Piloted Pitch Doublet Maneuver ...... 59 5.16 Utility Helicopter Response for Piloted Pitch Doublet Maneuver ...... 60 5.17 Utility Helicopter Load and Damage Results for Pitch Doublet Maneuver . . . . 60 5.18 Utility Helicopter Crack Length Growth Over Lifetime for Pitch Doublet Maneuver 61 5.19 Utility Helicopter Stick Inputs for the Piloted Roll Doublet Maneuver ...... 62 5.20 Utility Helicopter Attitudes for Piloted Roll Doublet Maneuver ...... 63

vii 5.21 Utility Helicopter Rates for Piloted Roll Doublet Maneuver ...... 64 5.22 Utility Helicopter Load and Damage Results for Roll Doublet Maneuver . . . . . 64 5.23 Utility Helicopter Crack Length Growth Over Lifetime for Roll Doublet Maneuver 65 5.24 Definitions of Bandwidth and Phase Delay Using Roll Attitude due to Lateral Cyclic as an Example ...... 66 5.25 Definitions of ∆φpk and ∆φmin for Moderate Amplitude Change ...... 67 5.26 Definition of Ppk for Moderate Amplitude Change ...... 67 5.27 Requirement for Small Amplitude Pitch Attitude Change at 120 knots Forward Flight for Utility Helicopter ...... 68 5.28 Requirement for Small Amplitude Roll Attitude Change at 120 knots Forward Flight for Utility Helicopter ...... 68 5.29 Requirement for Moderate Amplitude Pitch Attitude Change at 120 knots For- ward Flight for Utility Helicopter ...... 69 5.30 Requirement for Moderate Amplitude Roll Attitude Change at 120 knots Forward Flight for Utility Helicopter ...... 70 5.31 Heavy-Lift Transport Helicopter Control Inputs for Batch Pitch Doublet Maneuver 71 5.32 Heavy-Lift Transport Helicopter Attitude Response for Batch Pitch Doublet Ma- neuver ...... 72 5.33 Heavy-Lift Transport Helicopter Rate Response for Batch Pitch Doublet Maneuver 73 5.34 Heavy-Lift Transport Helicopter Response for Batch Pitch Doublet Maneuver . . 74 5.35 Heavy-Lift Transport Helicopter Stick Inputs for Piloted Pitch Doublet Maneuver 76 5.36 Heavy-Lift Transport Helicopter Attitude Response for Piloted Pitch Doublet Maneuver ...... 77 5.37 Heavy-Lift Transport Helicopter Rate Response for Piloted Pitch Doublet Maneuver 78 5.38 Heavy-Lift Transport Helicopter Response for Piloted Pitch Doublet Maneuver . 79 5.39 Requirement for Small Amplitude Roll Attitude Change in Forward Flight for Heavy-Lift Transport Helicopter ...... 80 5.40 Requirement for Small Amplitude Pitch Attitude Change in Forward Flight for Heavy-Lift Transport Helicopter ...... 81 5.41 Requirement for Moderate Amplitude Pitch Attitude Change in Forward Flight for Heavy-Lift Transport Helicopter ...... 81

A.1 Longitudinal Actuator Control ...... 84 A.2 Lateral Actuator Control ...... 84 A.3 Collective Actuator Control ...... 85 A.4 Pedal Actuator Control ...... 85 A.5 Dynamic Inversion Control Architecture ...... 86 A.6 Pitch Axis Compensator ...... 87 A.7 Pitch Axis Command Filter ...... 87 A.8 Pitch Axis Limiter ...... 88 A.9 Roll Axis Compensator ...... 88 A.10 Roll Axis Command Filter ...... 88 A.11 Roll Axis Limiter ...... 89 A.12 Dynamic Inversion Block ...... 90 A.13 Logic for Limiter Switch ...... 91

viii List of Tables

2.1 Utility Helicopter Basic Properties ...... 8 2.2 Gain Values for the Utility Helicopter ...... 9 2.3 Heavy-Lift Transport Helicopter Basic Properties ...... 21 2.4 Gain Values for the Heavy-Lift Transport Helicopter ...... 25

3.1 Command Filter Parameters ...... 34

ix List of Symbols

A Linearization State Matrix A Crack Growth Constant (mm/cycle)

A1 Lateral Actuator Angle (deg) B Input Matrix

B1 Longitudinal Actuator Angle (deg) CB−1 Control Mixing Matrix K Compensator

Nz Load Factor (g’s) P, Q, R Body Roll, Pitch, and Yaw Rate (rad/sec)

Rstress Stress Ratio S Stress (psi) V Airspeed (ft/sec) X Pilot Control Input (%) a Crack Length (mm) ~e Error Vector g Acceleration Due to Gravity (32.2 ft/sec2)

kn Controller Gain n Crack Growth Exponent ~r Reference Input u, v, w Body Forward, Right, Downward Velocities (ft/sec) ~u Control Vector

x ~x State Vector ~y Output Vector

θMR Main Rotor Collective Actuator Angle (deg)

θTR Tail Rotor Collective Actuator Angle (deg) α Stress Condition Constant

∆Keff Effective Stress Intensity Factor δ Control Input ζ Damping Ratio φ Roll Attitude (rad)

θ Pitch Attitude (rad) ψ Heading (rad) σ Stress (psi)

ωn Natural Frequency (rad/sec)

Subscripts col Collective

cmd Command f fast dynamics lat Lateral lng Longitudinal

ped Pedal s slow dynamics

Abbreviations ART Advanced Rotorcraft Technologies, Inc. ACAH Attitude Command Attitude Hold CSGE Control System Graphical Editor

DMC Damage Mitigation Control HUMS Health and Usage Monitoring System

xi PD Proportional Derivative PID Proportional Integral Derivative

SAS Stability Augmentation System TDA Technical Data Analysis, Inc.

xii Acknowledgments

First and foremost, I would like to thank my advisor, Dr. Joseph Horn, for his patience and support throughout this entire process. He has taught me a great deal over the past two years and I am grateful he gave me the opportunity to work with him. Second, a big thanks to Dr. Eric Keller for his assistance with the damage models. Thank you to retired USMC Colonel and Naval Aviator Michael O’Halloran for his willingness to fly the simulator and provide valuable feedback. I would also like to thank my girlfriend, Charlotte Cashell-Varga, for putting up with me and agreeing to move across the country to live in the snow with me. Lastly, I would like to thank my parents and grandparents for their support, both financially and emotionally over the past two years. They have been a constant source of encouragement and a significant part of getting me to where I am today.

xiii Chapter 1

Introduction

1.1 Motivation

Helicopters are highly complex systems which continually increase in complexity as new designs are envisioned and developed. Modern helicopters are used for a wide range of tasks in both the defense and civilian sectors and every task requires a safe, reliable, and cost effective aircraft.

Low maintenance time and cost are two crucial factors in determining the success of helicopter operations, however safety is still the main priority. The less time a helicopter spends being maintained, the more time it is able to safely and successfully perform its mission duties. As

fly-by-wire control systems become a commonplace in modern aircraft, controllers can be given more authority to improve the safety and longevity of the aircraft while reducing the workload of the pilot.

Improving aircraft longevity can be accomplished in several ways. One method is to increase the lifetime allowed by the components. This is ineffective as it would increase the risk of compo- nent failure and ultimately decrease the safety of the aircraft. Another option would be to install bulkier components. However, doing this would increase the overall structural weight and degrade the vehicle performance. A third option, and the most effective way to reduce the maintenance time, is through the assurance of component longevity by decreasing the high loads experienced by the aircraft components. By reducing these high loads, the components can be assured to last longer, requiring replacement less often. This can be accomplished through a damage mitigation controller that limits the pilot’s control inputs when necessary during aggressive maneuvers at 2 high airspeeds.

1.2 Background

In this research, the two helicopters studied were a heavy-lift transport helicotper similar to the

Sikorsky CH-53E Super Stallion and a utility helicopter similar to the Sikorsky UH-60 Black

Hawk. The CH-53E Super Stallion is currently the largest and heaviest helicopter in the United

States military. It is used primarily by the Marines for the transportation of heavy equipment and supplies. The UH-60 is a utility helicopter used by the army for many different opera- tions including troop and cargo transport, armed escort, medical evacuation, and even executive transport. The CH-53E can be seen in Figure 1.1 and the UH-60 is in Figure 1.2.

Figure 1.1. CH-53E Super Stallion (From Ref. [1])

Figure 1.2. UH-60 Black Hawk (From Ref. [2])

Both the CH-53E and the UH-60 have articulated main rotors. The rotor hub for these

helicopters allows the pilot to control the rotor blades through mechanical linkages. Pitch links

connect the swashplate to the rotor blades (through the pitch horn) and allow the pilot to pitch 3 the blades a desired amount. The scissor links keep the two parts of the swashplate from undesired rotation. The stationary scissors keep the lower swashplate rotating with the helicopter’s body while the rotating scissors keep the upper swashplate rotating with the rotor blades. A picture of the main rotor hub displaying these significant components can be seen in Figure 1.3. Damage to these components could result in a loss of vehicle control. The pitch link and pitch horn have been heavily investigated as they are both crucial to helicopter control and they experience high oscillatory loads, making them susceptible to fatigue damage. The stationary scissors have also been shown to experience high loads in flight, making them an interesting component to study.

Figure 1.3. Articulated Rotor Hub Showing Pitch Links and Stationary Scissors (from Ref. [3])

There have been numerous studies related to damage mitigation control of aircraft, both

fixed wing [4] and rotorcraft [5, 6, 7]. Some of these studies involved a reduction in fatigue

crack growth and taking preventative measures to ensure such damage would not shorten the

life of the components. Caplin et al. studied the effectiveness of a damage mitigating fly-by-

wire control system for an aircraft similar to the F-16. They concluded that the use of a damage

mitigation controller could potentially increase the wing fatigue life by 140% with no degradation

to handling qualities [4]. Similarly, Rozak [5] and Bridges [6] showed the effectiveness of damage

mitigation control for rotorcraft at high speeds and low speeds, respectively. Rozak concluded

that by adjusting the bandwidth of the controller in the pitch and yaw axes, the damage to the

pitch horn could be decreased with no effect on handling qualities. Bridges was able to reduce

the damage to the rotorcraft transmission using H2 and H∞ control synthesis for the heave, yaw, and rotor RPM degrees of freedom, while suffering only a slight degradation in handling qualities.

For an effective damage mitigation controller, damage to a specific component must be taken 4 into consideration. For example, Caplin et al. studied fatigue crack damage in the wing, Rozak studied the fatigue damage to the pitch horn, and Bridges studied fatigue crack damage in the transmission gears. There were a lot of data gathered on the pitch link loads during NASA’s

UH-60 Airloads Program [8], which was conducted in the late 1980s and early 1990s. Kufeld and

Bousman analyzed much of this data and their findings suggested that the high pitch link loads were primarily caused by dynamic stall on the rotor blade during agressive maneuvers and at high airspeeds [9]. Preventing blade stall from occurring would reduce the loads experienced by the pitch link and in turn reduce the damage accrued by the pitch link. Previous research has also shown that the pitch link experiences high oscillatory loads [10] which makes it an interesting component to study, especially for fatigue analysis and damage reduction.

A controller can be designed to limit the high structural loads experienced by the helicopter.

Examples of this can be seen in past work by Yavrucuk et al. [11], Sahani and Horn [12], and

Thaiss et al. [13]. Yavrucuk et al. created an envelope protection system for the unmanned helicopter, GTMax, at the Georgia Institute of Technology. This envelope protection system limited the structural loads experienced by the GTMax through load limiting control and blade stall protection. Since blade stall measurement is impractical for real world applications, an estimator was used to determine when blade stall occured. This estimator was based on the equivalent retreating indicated tip speed (ERITS) parameter, which is a function of airspeed, load factor, and rotor speed. Test data showed correlation of ERITS to blade stall such that as the

ERITS number decreased, the likelihood of blade stall increased. Using this ERITS value along with load factor limiting, an envelope protection system was developed and tested, successfully demonstrating prevention of large structural loads. Similarly, Sahani and Horn were concered with creating an envelope protection system for a UH-60 simulation model by converting the inner loop command constraints to constraints on the outer loop command. In doing so, the saturation limits were removed from the feedback loop, avoiding integrator wind up. This constrained the longitudinal and vertical axes by ensuring the torque limit would not be exceeded, except during short transients. Thaiss et al. developed a damage alleviation system for a utility helicopter.

A Health and Usage Monitoring System (HUMS) interface was developed to modify the control system outputs in real-time. With a damage model providing damage values, a dynamic inversion controller was created and gain scheduled with these damage values, allowing for the controller gains to vary as the damage rate changed. Simulation results showed that with this control law, 5 the damage to the pitch horn, swashplate, and the max damage rate all decreased [13]. It was also shown that damage reduction could be achieved with minimal change to the rotorcraft’s handling qualities with the implementation of this system. Modern control design techniques are an effective method for reducing loads and damage to helicopter components.

For this research a dynamic inversion controller was implemented. Dynamic inversion control has become a prevalent control methodology for aircraft over the past 30 years, as aircraft have become increasingly complex and computer technology has improved drastically [14, 15].

Dynamic inversion control laws take into account the non-linearities of the aircraft and allow for

flexibility and controller re-use for airframe variations. Instead of designing a compensator for every flight condition, as was the case for traditional control laws, a dynamic inversion controller allows one compensator design for use across the entire flight envelope. Using a known dynamic

flight model and state feeback, a dynamic inversion controller is much more robust and effective than traditional control methods [15]. These attributes make a dynamic inversion controller optimal for this research. The focus of this research was implementing load alleviation within a dynamic inversion controller and demonstrating improvements in component life.

1.3 Research Objective and Thesis Organization

This research investigates the effectiveness of a controller capable of reducing fatigue damage to critical helicopter components. The components of interest in this research were the pitch link, rotor shaft, and stationary scissors. These components were selected due to the high loads experienced during flight. Although there has been significant research in analyzing the pitch link loads, there has not been much work done in attempting to reduce the fatigue damage accrued by the pitch links. As stated earlier, there have been several studies where pitch link damage reduction was observed, but that was not the primary focus of those studies. This research sets out to assess the effectiveness of damage reduction to the pitch links, rotor shaft, and stationary scissors. The damage mitigation for this research is achieved through load alleviation by limiting the commanded response of the helicopter. By limiting the response accordingly, the critical components could experience lower forces, extending their fatigue life. This would reduce the cost and maintence of the helicopter as these components could be replaced less frequently and the helicopter could still operate safely with little to no degradation of handling qualities. The 6 handling qualities were evaluated using the ADS-33E requirements [16] for small and moderate amplitude changes in the pitch and roll axes. The two helicopters used for this research were large cargo and utility helicopters, so handling quality requirements for cargo and utility helicopters were used.

While past research has looked at load alleviation and damage mitigation, contributions from this research are listed as follows:

1. An increase in component life due to a load alleviating control system is shown.

2. The effect on roll and pitch axis handling qualities due to load alleviating control is shown.

3. A flexible blade model is used in the analysis, providing more accurate pitch link loads than

those a rigid blade model would produce.

4. The control design method could be generalized and extended to other aircraft, as evidenced

in this research by implementing the controller in two different helicopters.

The development and verification of the helicopter models using FLIGHTLAB will be dis- cussed in Chapter 2. In Chapter 3, the dynamic inversion controllers will be discussed, along with the damage mitigation control implementation. Chapter 4 will discuss the damage model for each helicopter. Chapter 5 will analyze the controller effectiveness through simulation results.

Finally, Chapter 6 will give concluding remarks and suggestions for future research. Chapter 2

Model Development

For this project, the FLIGHTLAB software developed by Advanced Rotorcraft Technology, Inc.

(ART) was used to create models of the utility helicopter and the heavy-lift transport helicopter.

Two models were created for the utility helicopter and one model was created for the heavy- lift transport helicopter. The heavy-lift transport model and one of the utility models were rigid blade models using blade element analysis for the main rotor. The second utility helicopter model used a flexible blade model for the main rotor. Both the rigid blade models and the flexible blade model employed articulated rotors.

2.1 FLIGHTLAB Software

The FLIGHTLAB software is an aircraft development and analysis program which allows users to produce highly detailed aircraft models from a library of modeling components using a graph- ical user interface [17, 18]. Once the FLIGHTLAB model is created, it can be analyzed using the Scope language, included with the FLIGHTLAB software. Analysis and simulation can be accomplished with predefined script files that are called through a point-and-click interface.

FLIGHTLAB has complex modeling capabilities for rotorcraft, making it particularly useful for rotorcraft analysis applications.

Other software packages developed by ART include the Control System Graphical Editor

(CSGE) and PilotStation. Both of these pieces of software enhance the capabilities of FLIGHT-

LAB. CSGE allows the user to create a block diagram controller for use with a FLIGHTLAB 8 aircraft model. PilotStation allows the FLIGHTLAB model to be run in a real-time simulation environment. However, Penn State has its own aircraft simulation environment that was used for this research. Details on Penn State’s simulation environment will be discussed in Chapter

5. The option to include or exclude certain software packages allows FLIGHTLAB to be very versatile and allows users to customize it specifically for their needs.

2.2 Utility Helicopter Development

A rigid blade and a flexible blade utility helicpoter model were developed using the FLIGHTLAB model editor. The rigid blade model used blade element theory on the main rotor. The flexible blade model used finite element analysis on the main rotor. The rigid blade model was developed as a base model to which the flexible blade model could be compared. The accurate calculation of rotor system loads requires flexible blade modeling, as this type of model allows blade root parameters to be obtained [19]. A list of basic vehicle properties for the utility helicopter can be seen in Table 2.1.

After the two models were developed, open loop control laws were implemented with CSGE.

The two models were compared to ensure that the vehicle responses were similar and that any discrepancies between the two models were expected or reasonable.

Property Value Number of Blades 4 Rotor Radius 26.83 ft Airfoil NACA 0012 Blade Twist -12.5 deg Blade Chord 1.73 ft Flap Hinge Offset 1.25 ft Lag Hinge Offset 1.25 ft Feathering Hinge Offset 1.25 ft Vehicle Mass 17,000 lbm Rotor Speed 258 rpm Tail Rotor Radius 5.5 ft

Table 2.1. Utility Helicopter Basic Properties

2.2.1 Rigid Blade Model

When developing a model using the FLIGHTLAB model editor, default values are provided.

These values correspond to a generic utility helicopter which is similar to the UH-60. For this 9 project, the default values were used for a majority of the vehicle. Wherever data was missing, or additional data was needed, data for the UH-60 was used. For these reason, it was safe to assume the utility helicopter should behave similarly to the UH-60.

The control mixing laws were created with CSGE using Equations 2.1, 2.2, 2.3, and 2.4.

The only coupling occured between the main rotor collective input and the tail rotor actuator.

The GENHEL model [20] was used as a reference in determining the control mixing gains, but ultimately the gains were determined to provide an appropriate vehicle response in both the time and frequency domains. The final gains for the utility helicopter are listed in Table 2.2.

θMR = k1 + k2Xcol (2.1)

B1 = k3 + k4Xlng (2.2)

A1 = k5 + k6Xlat (2.3)

θTR = k8 + k9Xped + k10Xcol (2.4)

The variables Xcol, Xlng, Xlat, and Xped represent the stick displacement in inches for col- lective, longitudinal cyclic, lateral cyclic, and pedal inputs, respectively.

Gain Value Gain Value k1 5.00 deg k6 1.60 deg/in k2 2.09 deg/in k8 6.00 deg k3 1.90 deg k9 5.30 deg/in k4 -2.88 deg/in k10 1.44 deg/in k5 0.00 deg Table 2.2. Gain Values for the Utility Helicopter

2.2.2 Flexible Blade Model

A flexible blade model of the utility helicopter was developed as well. To do this, detailed

structural blade data was required, most notably the bending stiffness, torsional stiffness, and

the mass radius of gyration for each axis. This data was collected from pages 84-86 in Reference

[21].

Using a flexible blade model allowed for the pitch link loads to be calculated directly by

FLIGHTLAB. For the utility helicopter, the pitch link was the only component for which an 10 accurate load model was attainable. (The rotor shaft and stationary scissor loads mentioned previously were specific to the heavy-lift transport helicopter analysis.) This research used a simple pitch link model, which treated the pitch link and pitch horn as a single component known as the pitch link assembly. This is appropriate for this work as both components experience similar loads.

The open loop control laws used for the rigid blade model were also used for the flexbile blade model. The gain values from Table 2.2 were used as well for consistency between the two models.

2.2.3 Response Characteristics

A frequency analysis was conducted on both the rigid blade and flexible blade models to ensure the linear model would be viable for the dynamic inversion control laws, discussed in Chapter 3.

Each model was trimmed at nine different airspeeds, ranging from 0 to 160 knots in increments of 20 knots. For each trim condition, the full order model was reduced to a nine state reduced order model. This was accomplished by first truncating the decoupled states such as the engine dynamics (assuming constant engine/rotor RPM through an RPM governor) and inertial position.

The remaining states could be split into two categories: “fast” dynamics and “slow” dynamics.

The “fast” dynamics, such as the flap and lag dynamics, actuator dynamics, and inflow dynamics were then cut from the model using the process shown in Equations 2.5 through 2.9.

        ˙ ~xs Ass Asf ~xs Bs   =     +   ~u (2.5)  ˙        ~xf Afs Aff ~xf Bf

˙ ~xf = 0 = Afs~xs + Aff ~xf + Bf ~u (2.6)

−1 ~xf = Aff (−Afs~xs − Bf ~u) (2.7)

˙ ~xs = Ared~xs + Bred~u (2.8)

−1 Ared = Ass − Asf Aff Afs (2.9)

This method left only the “slow” rigid body dynamics shown in Equation 2.10. The input 11

vector can be seen in 2.11.

 T ~xred = φ θ ψ u v w P Q R (2.10)

  ~u = δlng δlat δcol δped (2.11)

Once the matrices were reduced, a frequency analysis was conducted on each model to compare the full order model to its respective reduced order model. Figures 2.1 and 2.2 show the pitch and roll rate responses at 60 knots forward flight and Figures 2.3 and 2.4 show the pitch and roll rate responses at 120 knots forward flight. For damage mitigating control, the primary concern is the forward flight model, so hover and low speed responses were not critical in the analysis. The linear models show good correlation to the full order models in forward flight until the higher frequencies were reached. These descrepencies are due to the linearization taking into account only the rigid body states. The higher frequencies in the full order model are determined by the

“fast” rotor dynamics. Since the reduced order linear model was used in the dynamic inversion controller, which is designed to control the lower frequency rigid body dynamics, the discrepancies at high frequencies is acceptable.

The flexible blade model frequency responses show similar results in Figures 2.5 through 2.8.

The linear models closely match the full order models at lower frequencies and the two models only deviate at higher frequencies, due to the flexible rotor blades. The flexible blade model responses are quite similar to their rigid blade counterparts at 60 knots and 120 knots with only slight differences at very high frequencies. Overall, the similarities between the two models were sufficient. 12

Figure 2.1. Pitch Rate to Longitudinal Stick Frequency Response at 60 knots for the Rigid Blade Utility Helicopter

Figure 2.2. Roll Rate to Lateral Stick Frequency Response at 60 knots for the Rigid Blade Utility Helicopter 13

Figure 2.3. Pitch Rate to Longitudinal Stick Frequency Response at 120 knots for the Rigid Blade Utility Helicopter

Figure 2.4. Roll Rate to Lateral Stick Frequency Response at 120 knots for the Rigid Blade Utility Helicopter 14

Figure 2.5. Pitch Rate to Longitudinal Stick Frequency Response at 60 knots for the Flexible Blade Utility Helicopter

Figure 2.6. Roll Rate to Lateral Stick Frequency Response at 60 knots for the Flexible Blade Utility Helicopter 15

Figure 2.7. Pitch Rate to Longitudinal Stick Frequency Response at 120 knots for the Flexible Blade Utility Helicopter

Figure 2.8. Roll Rate to Lateral Stick Frequency Response at 120 knots for the Flexible Blade Utility Helicopter 16

The frequency responses were compared to flight test data for the UH-60 at 80 knots forward

flight. The flight tests were conducted at 80 knots forward flight with the SAS and Flight Path

Stabilization system disengaged. The roll and pitch rate frequency responses were identified using the CIFER software package [22]. The roll rate frequency response to a lateral input comparison between the FLIGHTLAB full order flexible blade model and the UH-60 test data can be seen in Figure 2.9. This shows a reasonable correlation between the two responses.

Figure 2.9. Roll Rate to Lateral Stick Comparison of Utility Helicopter to Test Data at 80 knots from Reference [22]

Several other tests were conducted to ensure accuracy of the flexible blade model. The

trimmed stick positions for various airspeeds were computed for both the rigid blade and flexible

blade models and the comparison of these two models can be seen in Figure 2.10. Note the

collective and lateral stick inputs are higher for the flexible blade model. For collective, this

was expected as the rotor blades tend to twist leading edge down with a flexible blade model,

requiring a higher blade pitch than a rigid blade model to achieve the equivalent lift.

Short time histories were used to compare the models as well. Because the models are using

open loop control, they will go unstable after a short period of time, thus requiring the short time

interval. The input command for the time histories can be seen in Figure 2.11. The commanded 17 input was the same for each axis but the tests were conducted independently to see the response to a single control input (e.g. lateral cyclic was perturbed while all other controls remained in trim position to see the roll response): a five percent step input beginning at two seconds and lasting for three seconds. The on-axis attitude responses can be seen in Figure 2.12 and the on- axis rate responses can be seen in Figure 2.13. Very little difference between the two models was observed. The rigid blade model was slightly quicker to respond to the control inputs, although not by much. This is due to the additional phase delay in the flexible blade model as well as the torsional deflection resulting in a lower equivalent blade pitch. The similarities between the two models indicate that the flexible blade model was sufficient to use for the damage mitigation analysis throughout the rest of this research.

Figure 2.10. Trimmed Stick Position Comparison for Rigid Blade and Flexible Blade Utility Helicopter Models 18

Figure 2.11. Stick Input for Time Histories 19

Figure 2.12. On-Axis Attitude Response Comparison of Rigid and Flexible Blade Models at 120 knots 20

Figure 2.13. On-Axis Rate Response Comparison of Rigid and Flexible Blade Models at 120 knots 21

2.3 Heavy-Lift Transport Helicopter Development

A rigid blade heavy-lift transport helicopter model was developed concurrently with the utility helicopter rigid blade model. Open loop control laws were implemented with CSGE and this model’s response characteristics were verified in the time domain using flight test data. The model was also verified using public domain data on the trim characteristics and frequency response.

2.3.1 Flight Model

The heavy-lift transport helicopter model was developed primarily from data available to the public. Many of the geometric properties for the fuselage and tail rotor were taken from Jane’s

All the World’s Aircraft, 2001-2002 [23] for the CH-53E. Basic geometric properties for the main rotor came from this source as well. For data that was not publicly available, publicly available data for the CH-53C was scaled up appropriately. A list of properties for the heavy-lift transport helicopter can be found in Table 2.3.

Property Value Number of Blades 7 Rotor Radius 39.5 ft Airfoil SC10951 Blade Twist -10 deg Blade Chord 2.4 ft Flap Hinge Offset 2.5 ft Lag Hinge Offset 2.5 ft Feathering Hinge Offset 3.3 ft Vehicle Mass 46,500 lbm Rotor Speed 187 RPM Tail Rotor Radius 10 ft

Table 2.3. Heavy-Lift Transport Helicopter Basic Properties

To accurately model the fuselage airloads, FLIGHTLAB required a table lookup for the lift, drag, and side forces as well as the roll, pitch, and yaw moments with respect to angle of attack and sideslip angle. These tables were created by modifying the airload tables provided for the

CH-53C in A Mathematical Model of the CH-53 Helicopter [24]. This report only provided two- dimensional plots for the forces and moments vs angle of attack and separate plots for the forces and moments vs sideslip. Examples of these plots are shown in Figures 2.14 and 2.15. Note the sideslip was given as a wind tunnel yaw axis, so the signs needed to be flipped to get the proper 22 sideslip data. This data was extracted using plot digitizing software and the plots were summed to create two-dimensional table look-ups for each force and moment. For example, the data from

Figures 2.14 and 2.15 were summed to produce the plot seen in 2.16. Another example shows how Figures 2.17 and 2.18 sum to produce Figure 2.19. The data used to produce Figures 2.16 and 2.19 were used in the FLIGHTLAB model. Because of the geometric differences between the ’C’ and ’E’ models of the CH-53, the tables were scaled by surface area and then fine tuned to match the flight test data.

Figure 2.14. Fuselage Incremental Rolling Figure 2.15. Fuselage Incremental Rolling Moment as a Function of Angle of Attack Moment as a Function of Sideslip (Wind Tun- nel Yaw Angle) 23

Figure 2.16. Fuselage Roll Moment as a Function of Angle of Attack and Sideslip

Figure 2.18. Fuselage Incremental Lifting Force as a Function of Sideslip (Wind Tunnel Yaw Angle)

Figure 2.17. Fuselage Incremental Lift- ing Force as a Function of Angle of Attack 24

Figure 2.19. Fuselage Lift Force as a Function of Angle of Attack and Sideslip 25

2.3.2 Open Loop Control

Once the FLIGHTLAB model was fully developed in the model editor, an open loop controller was created with CSGE to verify the model against the flight test data provided by TDA [25].

The control mixing laws used for the CH-53C were provided in Reference [24] and it was assumed that the ’E’ model used similar control mixing. Three of the equations were identical to those used by the utility helicopter model (Eq. 2.1, Eq. 2.2, and Eq. 2.4) while the fourth equation, shown in Eq. 2.12, was similar to Eq. 2.3. Note the only difference is the addition of a term coupling the collective stick to the roll actuator. The gain values, kn, were tailored so that the vehicle response matched the flight test data. The final gain values can be seen in Table 2.4.

A1 = k5 + k6Xlat + k7Xcol (2.12)

Gain Value Gain Value k1 8.50 deg k6 1.35 deg/in k2 1.44 deg/in k7 -0.144 deg/in k3 3.00 deg k8 1.50 deg k4 2.13 deg/in k9 5.30 deg/in k5 -1.00 deg k10 1.44 deg/in Table 2.4. Gain Values for the Heavy-Lift Transport Helicopter

2.3.3 Model Verification and Response Characteristics

The heavy-lift transport helicopter was verified in a couple ways. The first, mentioned above, was to compare the time histories to the flight test data, although the comparison is not shown here as some of the data is not in the public domain. The second was to compare the model to the Naval Air Training and Operating Procedures Standardization Program (NATOPS) manual for the CH-53E [26]. An airspeed sweep was conducted and the results for the trimmed pitch attitude can be seen in Figure 2.20 and the required torque can be seen in Figure 2.21. The pitch attitude shows decent correlation to the NATOPS manual, aligning closely with the forward CG curve. The torque curve also matched closely, only differing by 3-5% torque. Once the vehicle model was determined to be sufficient, a frequency analysis was conducted. Like the utility helicopter model, this was done to ensure that the linearized reduced order model could be used in the dynamic inversion controller to accurately represent the full order model. 26

Figure 2.20. Trimmed Pitch Attitude Comparison of FLIGHTLAB Model with NATOPS Report

Figure 2.21. Trimmed Torque Requirement Comparison of FLIGHTLAB Model with NATOPS Report 27

The linearized model was the same nine state reduced order model used for the utility he- licopter, using the rigid body states seen in Equation 2.10. The full order model included the rigid body dynamics, flap and lag dynamics, inflow dynamics, and engine dynamics.

The system was converted into state space form and frequency response plots were produced.

Figures 2.22 and 2.23 show the frequency response comparisons for the heavy-lift transport helicopter at 60 knots forward flight for both the pitch and roll rates. Figures 2.24 and 2.25 show the frequency response comparisons at 120 knots. In all cases, the linearized low frequency responses closely correlated to their respective full order models. There were small variations in the high frequency region, however these variations were insignificant as this research focused primarily on the low frequency response.

Figure 2.22. Pitch Rate to Longitudinal Stick Frequency Response at 60 knots for the Heavy-Lift Transport Helicopter 28

Figure 2.23. Roll Rate to Lateral Stick Frequency Response at 60 knots for the Heavy-Lift Transport Helicopter

Figure 2.24. Pitch Rate to Longitudinal Stick Frequency Response at 120 knots for the Heavy-Lift Transport Helicopter 29

Figure 2.25. Roll Rate to Lateral Stick Frequency Response at 120 knots for the Heavy-Lift Transport Helicopter

The frequency responses for the heavy-lift transport helicopter were compared to frequency responses for the CH-53E from Reference [27]. Good correlation can be seen in Figures 2.26 and

2.27, which shows the roll response due to lateral input. 30

Figure 2.26. Roll Rate to Lateral Stick Frequency Response Comparison Between the Heavy-Lift Transport Helicopter FLIGHTLAB Model and Test Data in Hover from Reference [27]

Figure 2.27. Roll Rate to Lateral Stick Frequency Response Comparison Between the Heavy-Lift Transport Helicopter FLIGHTLAB Model and Test Data at 70 knots from Reference [27] Chapter 3

Controller Design

Dynamic inversion control laws were used for all helicopter models in this research. Dynamic inversion control is suitable for a wide range of flight conditions without the need to gain schedule different controllers. Dynamic inversion control also allows small changes to be made to the vehicle without the need to redesign the entire controller. An overview of dynamic inversion control laws will be presented, followed by a detailed description of the controllers used in this research.

For damage mitigation, a load limiting control design was used. Through this method, the roll and pitch rates could be limited to ensure the vehicle would not exceed specified values which would cause excessive loads to the components in question. Determination of these values was conducted by running simulations without damage mitigation control to see which factors had the greatest influence on loads and damage rates of the specific components.

3.1 Dynamic Inversion Control Law

Dynamic inversion control laws eliminate the need for designing different controllers for each

flight condition the vehicle will experience. To create a dynamic inversion controller, the system should be modeled in state space form as seen in Equations 3.1 and 3.2.

~x˙ = A~x + B~u (3.1) 32

~y = C~x (3.2)

The matrices A, B, and C are functions of the flight condition and can be scheduled with slowly varying variables (airspeed in this case). The state vector is denoted by ~x, the input vector is

~u, and the output vector is ~y. For this control method to work, it is assumed that it is a square system (i.e. vectors ~u and ~y have the same dimensions). If this is untrue, a different design approach must be taken.

The output ~y can then be differentiated as in Equation 3.3 so that the control ~u appears in the derivative expression.

~y˙ = C~x˙ = CA~x + CB~u (3.3)

If CB = 0, then the equation must be differentiated again. Differentiation should continue until the coefficient for ~u is nonzero.

For the square system, the output ~y should be controlled by following a desired reference trajectory (~r). This will produce the tracking error ~e shown in Equation 3.4, and its derivative

~e˙ shown in Equation 3.5.

~e = ~r − ~y (3.4)

~e˙ = ~r˙ − ~y˙ (3.5)

Substituting Equation 3.3 into Equation 3.5 yields

−~e˙ = CA~x + CB~u − ~r˙ (3.6)

Some form of compensation must be used to minimize this tracking error. A supplemental input, ν, can be defined as

ν = −~e˙ (3.7) and it can be related to some type of compensation (K) to stabilize the system in the form of

ν = K~e = −~e˙ (3.8)

By substituting Equation 3.8 into Equation 3.6, the control ~u can be solved for as seen in Equation

3.9 and a diagram of this control law is shown in Figure 3.1. Note that the aircraft dynamics are 33 built into the controller, which is why the linearized aircraft model was required.

~u = CB−1[ −CA~x + ~r˙ + K~e ] (3.9)

Figure 3.1. Dynamic Inversion Control Law Architecture

For the compensator acting on the error (K), any form of compensation can be used in con- juction with the dynamic inversion control law. Classical control methods such as proportional- derivative (PD) and proportional-integral-derivative (PID) are quite common. These feedback control methods are simple to design and easy to implement.

3.2 Implementation and Response Type

The control architecture used in CSGE was taken from a controller designed for a tiltrotor aircraft

[28] using linear dynamic inversion control. Several modifications were made to the controller so that it would work with the utility and heavy-lift transport helicopter models. The most significant change was incorporating an integrator in the roll and pitch axis compensators, altering the control compensation from PD to PID. Before this alteration, poor response characteristics were observed for the conventional helicopter designs. Other changes made were primarily model specific (e.g. linear models, command filter gains) without altering the architecture. The final controller diagrams can be found in the Appendix.

The open loop control laws coupled with the dynamic models described earlier in Section 2.3.2 were used to create linear models of each helicopter. The full order models were linearized about different airspeeds ranging from from 0 to 160 knots in 20 knot increments. This provided nine linearized models from which the state space matrices could be extracted and implemented in the dynamic inversion controller. The controller linearly interpolated for airspeeds not explicitly 34 stated.

Selection of a response type is crucial when designing a control system. The response type is characterized by transfer functions in the command filter. One common response type for rotorcraft is Attitude Command / Attitude Hold (ACAH). ACAH response directly correlates a control/stick displacement to a vehicle attitude, as seen by the second order transfer function in

Equation 3.10. This was the type of transfer function used in the roll and pitch axes. A first order transfer function like the one in Equation 3.11 was used for the yaw axis. The vertical axis was left as open loop control. 2 θ Cωn = 2 2 (3.10) δ s + 2ζωns + ωn R C = (3.11) δ τs + 1

In Equation 3.10, θ represents the vehicle attitude and δ represents the control input. R represents the vehicle yaw rate in Equation 3.11. C is a unit conversion constant, relating the stick displacement (%) to either the vehicle attitude (rad) or the vehicle Euler rate (rad/s), depending on the order of the transfer function. The natural frequency and damping ratio were selected to exceed Level 1 handling qualities according to ADS-33. Table 3.1 lists these parameters for both vehicles in each axis.

Utility Heavy-Lift Transport Helicopter ωn,roll 2.0 rad/sec 3.0 rad/sec ζroll 0.9 1.0 Croll 0.0314 rad 0.0157 rad ωn,pitch 2.0 rad/sec 2.0 rad/sec ζpitch 0.7 0.8 Cpitch 0.0105 rad 0.0105 rad τyaw 4.0 sec 4.0 sec Cyaw 0.644 rad/sec 0.644 rad/sec Table 3.1. Command Filter Parameters

One note is that the yaw axis incorporates turn coordination. Below 40 knots, the yaw rate command is dictated entirely by the pedal inputs. Above 60 knots, the yaw rate command is dictated entirely by Equation 3.12, so the Cyaw value is different for low speeds and high speeds. Between 40 and 60 knots, blending between the two (pedal input and Equation 3.12) occurs to determine the yaw rate command. In Table 3.1, the value listed is for forward flight (>60 knots). 35

C δ + g sin(φ) cos(θ) R = yaw ped (3.12) cmd V

3.3 Load Limiting Control and Logic

The damage reduction to the hub components was achieved through load limiting control. These loads are not practically measured values in a real flight environment and are not directly con- trolled by the flight control system, so a correlation was made between the component loads and the state variables. These state variables could be limited to specified values, which would effectively limit the loads experienced by the pitch link.

The limiter could be toggled on or off by the pilot during flight. This would allow the pilot to determine when damage mitigation control (DMC) was necessary or beneficial, while simultaneously allowing the pilot to fly the vehicle unaltered if necessary. The DMC could also be automated to automatically trigger depeding on the mission and condition of the aircraft.

The toggle switch control logic, implemented in CSGE, can be seen in Figure A.13.

3.3.1 Utility Helicopter Limits

For the utility helicopter, the pitch link was the component in question. Several factors con- tributed to the high pitch link loads. The two primary contributors were the roll rate and the load factor. By limiting these values, the pitch link load was reduced. However, a relationship between the load factor and the vehicle states was required, as the load factor could not be directly limited. The pitch rate is related to the load factor through the relationship seen in

Equation 3.13. By limiting the pitch rate, the load factor could be effectively be limited.

(N − 1)g z = Q (3.13) V lim

In this equation, g is the force of gravity and V is the aircraft velocity. Qlim is the limited pitch rate value and using this relation, a load factor, Nz, could be specified to limit the pitch rate. This was accomplished by altering the command filter in Figure 3.2 to incorporate a pitch rate limiter. The full pitch rate limiter block diagram is in Figure A.8 of the appendix.

The rate limiter works using the conditional statement in equation 3.14. If the pitch acceler- 36

Figure 3.2. Command Filter with Rate Limiter ation command is positive and the difference between the pitch rate command and the limiting pitch rate is also positive, then the pitch acceleration command is set to zero. If these conditions are not met, the pitch acceleration command is unaltered.

Q˙ cmd > 0 ∩ (Qcmd − Qlim) > 0 ⇒ Q˙ cmd = 0 (3.14)

Rotor loads are a complex phenomenon based on many physical parameters. However, it can be shown that the peak-to-peak loads are strongly correlated with a few basic aircraft states.

To determine appropriate load factor limits, several tests cases were run using aggressive flight control inputs at various airspeeds. An example of the pitch link load in steady, level flight at

120 knots is shown in Figure 3.3 and the pitch link load during an aggressive pitch maneuver is shown in Figure 3.4. In Figure 3.3, it can be seen that the pitch link undergoes an oscillatory cycle just over four times per second. In steady, level flight the pitch link experiences a peak- to-peak load of around 500 pounds during one cycle. During an aggressive maneuver, the load increases. Figure 3.4 shows the cycle with the largest peak-to-peak load occurring between 6.2 and 6.4 seconds, varying from 100 pounds to -1200 pounds. These loads occurred where the load factor was the greatest, which can be seen in Figure 3.5. By limiting the load factor, these high peak-to-peak loads could be reduced, which would reduce the damage to the pitch links.

Figure 3.6 shows the peak-to-peak load versus load factor. It is clear that this relationship is nonlinear and limiting the load factor would reduce the peak-to-peak loads. Limiting the vehicle to 1.6 g’s during high speed flight would have provided the greatest reduction to the pitch link loads. However, setting the limit this low caused a significant loss in handling qualities and maneuverability. It was determined that 1.8 g’s provided the greatest benefit to pitch link longevity without causing significant loss to the handling qualities or maneuverability. 37

Figure 3.3. Pitch Link Load in Steady Level Flight at 120 knots

Figure 3.4. Pitch Link Load During Aggressive Maneuver at 120 knots

The other major contributing factor to the high pitch link loads was the roll rate. Since this is a state variable, the roll rate could be limited directly, eliminating the need to find a related variable to represent it, as was the case for the load factor/pitch rate. The limiter was implemented in the command filter in the same manner as the pitch rate limiter shown in Figure

3.2. Parameter sweeps were conducted to determine the appropriate roll rate limits at various airspeeds. The results of these tests are shown in Figure 3.7. This shows that a roll rate limit of 0.8 rad/sec was appropriate for 90 knots and 0.4 rad/sec was appropriate for 150 knots and higher. These values were selected and the limit was interpolated linearly between these two points. Although not shown in Figure 3.7, negative roll rates greater than 0.8 rad/sec produced high pitch link loads only at airspeeds greater than 140 knots. For this reason, a negative roll limit of 0.8 rad/sec was placed on airspeeds greater than 140 knots. 38

Figure 3.5. Load Factor Time History for Various Airspeeds

Figure 3.6. Load Factor Limit Determination for Pitch Link Load at Various Airspeeds 39

Figure 3.7. Roll Rate Limit Determination for Pitch Link Load at Various Airspeeds

3.3.2 Heavy-Lift Transport Helicopter Limits

The heavy-lift transport helicopter research focused on reducing loads for aggressive pitch ma- neuvers only. The roll command was not limited as the loads model for the heavy-lift transport helicopter (discussed in Section 4.2) did not take the roll states into account. Since three compo- nent loads were available, limits were determined based on the most stringent limit of the three components. The limit determination plots for this helicopter could not be shown as they include data not available in the public domain.

The positive pitch rate limit and load factor were determined by the pitch link loads. At lower airspeeds (<120 knots), the load factor linearly increased with the pitch link loads. By limiting the load factor at these airspeeds, a lower damage rate could be achieved, but a maneuver would take longer to complete when compared to a case without damage mitigation control. This lower damage rate would be sustained for a longer period of time and would actually cause more damage to the pitch link than the non-limited case of a high damage rate for a very short period of time.

This indicated that load factor limiting was ineffective in this region as more damage would be caused to the pitch links. The benefits of load factor limiting came in the higher airspeed region, where the curves showed nonlinear trends. By limiting the load factor at high airspeeds, effective 40 damage mitigation was achieved for the positive pitch command.

The negative pitch command limit was implemented using a pitch acceleration limiter. High negative pitch accelerations correlated to high shaft bending loads. When these negative pitch accelerations were limited, the shaft bending loads were greatly reduced. Chapter 4

Damage Model

To study the effectiveness of a damage mitigation controller, a model must be developed to estimate the damage to the vehicle component. Two different damage models were used in this research, one for each vehicle. The utility helicopter implemented a fatigue crack growth model.

Assuming a small crack exists in the component, this model predicts the growth rate of the crack. The heavy-lift transport helicopter used a damage model that used S-N curves to convert estimated component loads to damage values. This model was developed by Technical Data

Analysis, Inc. (TDA) and implemented using CSGE.

4.1 Utility Helicopter

The pitch link has one of the shortest replacement intervals according to the Sikorsky Aircraft specification SER-70114 for the Black Hawk helicopter [5]. This makes the pitch link an inter- esting component to study for damage evaluation as increasing the component life would reduce maintenence costs and vehicle down time.

To determine the component damage, a component structural model and damage model were necessary. The damage model will be discussed first, as that dictates the required parameters needed from the structural model. The structural model will then be discussed. 42

4.1.1 Fatigue Crack Growth Model

In this research, a Linear Elastic Fracture Mechanics model proposed by Newman was used [29].

In ductile metals undergoing variable cyclic loads, it has been shown that crack opening stress

can have a significant effect on the fatigue life of a component. This factor contributes to the

inaccuracy of traditional methods of life prediction under variable cyclic loading. Under fatigue,

a plastic zone forms at the tip of the crack. At stresses below the crack opening stress, the

deformed material in the plastic zone compresses the crack tip, and thus the crack does not

grow. Under uniform loading, the crack opening stress reaches a steady state value that changes

slowly as the crack grows. However, two competing factors in variable loading effect the crack

opening stress in such a way that the order of application of load cycles is important for accurate

life prediction. Overloads will cause an initial increase in crack growth, but also increase the

plastic zone size. This increases the crack opening stress. Any subsequent load cycles will result

in less crack growth than would have been the case if the overload had not occurred [30, 31].

The other factor affecting crack opening stress is load reversal. When the material in the plastic

zone is compressed past the compressive yield stress, it will be deformed in such a way that it

no longer compresses the crack tip to the same degree. This lowering of the crack opening stress

causes an acceleration of the crack growth rate. If overloads and load reversals occur at random

intervals, the crack growth rate will vary significantly from the rate assumed by methods that

do not take crack opening stress into account [32].

Equations 4.2 through 4.10 show Newman’s crack growth model. The material used in this

research was Aluminum 7075-T6, a high strength aluminum, as this material closely resembles the

actual Black Hawk pitch link material [5]. The material properties were used in the calculation

of the flow stress in Equation 4.1. The values for yield stress (σy) and ultimate stress (σult) were 73 ksi and 83 ksi, respectively [33]. The first step to calculating the crack growth was to determine the crack opening stress for the given cycle, So. One cycle was defined as one complete revolution of the main rotor.

1 σ = (σ + σ ) (4.1) 0 2 y ult

Smin Rstress = (4.2) Smax 43

  1/α 2 πSmax A0 = (0.825 − 0.34α + 0.05α ) cos (4.3) 2σ0

Smax A1 = (0.415 − 0.071α) (4.4) σ0

A3 = 2A0 + A1 − 1 (4.5)

A2 = 1 − A0 − A1 − A3 (4.6)   Smax(A0 + A1Rstress) if Rstress < 0 So = (4.7) 2 3  Smax(A0 + A1Rstress + A2Rstress + A3Rstress) if Rstress ≥ 0

After the crack opening stress was calculated, it was compared to the maximum stress expe-

rienced during the current cycle. If the current cycle stress was larger than the crack opening

stress, the crack growth rate was determined based on Equations 4.8 through 4.10. If the current

cycle stress was lower than the crack opening stress, the crack length remained constant.

Sinc = Smax − max(So,Smin) (4.8)

√ ∆Keff = Sinc πa (4.9)  da  0 if Smax < So = (4.10) dN n  A(∆Keff ) if Smax ≥ So

The resultant crack growth rate could then be used to determine the accumulated damage by adding it to the existing crack length.

4.1.2 Component Loads and Structural Model

The pitch link loads were calculated directly through FLIGHTLAB using the flexible blade model with a simple pitch link. The axial load was considered, as this was the dominant load. This load vector was used as the total load on the pitch link.

The maximum stress on the pitch link occurrs where the pitch link attached to the pitch control horn [5]. The load can be related to the maximum stress using the relationship provided in Equation 4.11, where Fpitchlink is in pounds and S is in psi. For each cycle, an array of stresses was produced using this relation. The maximum and minimum stresses, Smax and Smin, were gathered from each cycle and used in Equation 4.2 in the damage model. 44

S = −6.55 × Fpitchlink (4.11)

4.2 Heavy-Lift Transport Helicopter Damage Model

Discussion of the heavy-lift transport helicopter damage model is limited, as it was developed by

TDA and some of the data used is not in the public domain. Implementation of the damage model was done through CSGE and the values were calculated during the simulations. The damage model contained two parts. The first was a peak-to-peak load response for each of the three components (pitch link, rotor shaft, and stationary scissors) while the second part calculated the component damage as modeled by Palmgren-Miner’s rule via component S-N curves [34].

The loads model assumed there was no direct measurement of loads on the rotor hub. The model was developed using MH-53E flight test data, where system identification methods were used to predict the loads from aircraft states: load factor, airpseed, angular rates, and angular accelerations. A least squares fit method was used to create a mathematical model relating the aircraft states to the peak-to-peak loads of each component.

Once the peak-to-peak load response was determined, Palmgren-Miner’s rule was used to translate the load to a damage rate for each component. Since S-N curves were used to determine the damage rate per cycle, the maximum load was gathered and stored for a given cycle. Once the azimuth crossed zero (at the end of each cycle), the corresponding damage rate was caluclated and the maximum load was reset. Chapter 5

Simulation and Evaluation

Two types of simulations were run: batch simulations and real time piloted simulations. The batch simulations were run using the FLIGHTLAB software and were run to better understand the vehicle response in an ideal, controlled environment. The piloted simulations were run in the Penn State Flight Simulation Facility. The piloted simulations were run to see the damage mitigation effects in a realistic environment and to receive a qualitative evalutation from the pilot.

The component loads and damage were gathered during both batch and piloted simulations. For the utility helicopter, only the pitch link was analyzed. For the heavy-lift transport helicopter, the pitch link, rotor shaft, and stationary scissors were analyzed.

The handling qualities were investigated with and without the damage mitigation controller to determine the potential risks of altering the pilot input. Ideally, no change in handling qual- ities would be observed when the damage mitigation was engaged. The handling qualities were assessed using the ADS-33E requirements for small and moderate amplitude changes in forward

flight for the roll and pitch axes.

5.1 Simulation Environment

5.1.1 Simulator Hardware

The Penn State Flight Simulation Facility is a fixed-base simulator utilizing the cockpit of a

Bell XV-15 tilt-rotor prototype. It is outfitted with a four-channel, 300lb capable control loading 46 system to provide programmable force-feel characteristics to the pilot. The displays are projected onto a 15 foot diameter cylindrical screen with a height of 10 feet and a 170 degree field of view.

Within the cab are a set of monitors for customizable instrument displays. The flight simulator is shown in Fig. 5.1.

Figure 5.1. Flight Simulator at The Pennsylvania State University

5.1.2 Simulator Software

The imagery for the flight simulator is generated by X-Plane, a flight simulation software. X-

Plane provides global scenery, customizable weather, and the ability to implement custom scenery.

X-Plane has a large online community for technical support, making it easy to resolve any issues or install custom aircraft models and scenery.

A custom plug-in was used to integrate X-Plane with the flight dynamics model. The plug- in receives aircraft position and attitude values through a shared memory block, allowing the appropriate graphics to be generated.

For this research FLIGHTLAB generated the flight dynamics model. Using shared memory blocks, FLIGHTLAB would receive control inputs from the simulator and send the vehicle re- sponse data to X-Plane for graphics generation. The FLIGHTLAB model also interacted with a 47 supplemental C++ program written primarily to record data to an output file for post processing.

5.2 Simulation Method

The helicopter models were flown in both batch and piloted simulations. The batch simulations were run for several reasons. One major reason was to see what types of loads would be expe- rienced and to set the limiters to appropriate levels for effective damage mitigation. Through the batch simulations, many tests could be run in a short time to collect a large amount of data. One major setback of using only batch simulations was that realistic inputs could not be easily produced. One control input was perturbed while the other three remained constant. The piloted simulations solved this dilemna. By having a pilot flying the vehicle, all controls could be controlled in a realistic manner. Another benefit of conducting piloted simulations was to understand how a pilot responds when the damage mitigation controller was implemented. The piloted simulations also allowed a full maneuver to be run without timing the inputs. The pilot would fly the vehicle until the maneuver was finished as opposed to the batch simulations where the inputs were strictly timed, even if the maneuver was not completed. This was evident in the results. A former Marine helicopter pilot conducted the piloted simulations and provided feedback on both helicopters.

Tests were conducted by trimming the rotorcraft at 120 knots forward flight, as that airspeed was shown to cause the most damage to the components of interest. The maneuvers simulated were roll and pitch doublets as these maneuvers were shown to produce high loads to the hub components. The results will be shown for each helicopter in their respective sections.

The piloted simulations were conducted in the Penn State Flight Simulation Facility. The pilot did his best to ensure the rotorcraft trajectory was similar for each run to provide the best comparison of the data. Given a more realistic scenario with the piloted simulations, a better understanding of the damage reduction could be observed while conducting real time simulations. 48

5.3 Utility Helicopter Simulation

5.3.1 Loads and Damage Reduction

5.3.1.1 Batch Simulations

The batch simulations showed a slight benefit to using damage mitigation control for the pitch links on the utility helicopter. Roll and pitch doublets were run, following the control inputs shown in Figure 5.2 and 5.3.

Figure 5.2. Stick Inputs for the Batch Pitch Doublet Simulations 49

Figure 5.3. Stick Inputs for the Batch Roll Doublet Simulations

The vehicle response to the pitch doublet is in Figures 5.4 through 5.6. Figure 5.7 shows a slight reduction to the load and crack growth. This slight reduction is nearly insignificant short term, but shows a slight improvement to component life long term. Figure 5.8 shows this improvement. This was determined by running the same pitch doublet maneuver 5,000 times to represent repetitive flight operations over the lifetime of the pitch link. The crack length began at 2 mm. When damage mitigation control was on, the crack length only grew an additional 0.1 mm. This is 29% of the crack growth of 0.35 mm when DMC was not used. 50

Figure 5.4. Utility Helicopter Attitude Response to Pitch Doublet Maneuver 51

Figure 5.5. Utility Helicopter Rate Response to Pitch Doublet Maneuver 52

Figure 5.6. Utility Helicopter Response to Pitch Doublet Maneuver

Figure 5.7. Utility Helicopter Pitch Link Loads and Crack Growth for Pitch Doublet Maneuver 53

Figure 5.8. Utility Helicopter Crack Growth Over Pitch Link Lifetime from Repeated Pitch Doublet Maneuvers 54

Limiting the roll rate showed promising results to using DMC as well. The vehicle responses to the roll doublet maneuver are in Figures 5.9 through 5.10. The load and damage results to this maneuver are in Figure 5.11. As mentioned in Chapter 4, the crack opening stress decreases over time with many load reversals, causing lower loads to produce equivalent crack growth. Although the crack growth difference is almost negligible for a single maneuver (as was the case for the pitch axis as well), the long term effects are much more prominent for repeated roll maneuvers.

Here we see a slight decrease to the single maneuver crack growth rate when the DMC is engaged, similar to what was seen for the pitch maneuver. After 5,000 repeated maneuvers, the crack grew by 1 mm without DMC and a nonlinear trend can be seen, indicating that the crack will begin to grow much quicker. When DMC was used, the crack only grew an additional 0.45 mm, giving a 55% reduction in the crack length over the same span.

Figure 5.9. Utility Helicopter Attitude Response to Roll Doublet Maneuver 55

Figure 5.10. Utility Helicopter Rate Response to Roll Doublet Maneuver

Figure 5.11. Utility Helicopter Pitch Link Loads and Crack Growth for Roll Doublet Maneuver 56

Figure 5.12. Utility Helicopter Crack Growth Over Pitch Link Lifetime from Repeated Roll Doublet Maneuvers

5.3.1.2 Piloted Simulations

The real time piloted simulations show long term damage reduction to the pitch links. The piloted simulations used a terrain following pitch doublet maneuver to represent a typical maneuver a pilot might encounter. The vehicle was initialized in a trimmed condition at 120 knots over a hill. The pilot pushed the stick forward, following the downward slope of the hill. Upon reaching the base of the hill, the pilot pulled up along an adjacent hillside. The pilot stick inputs to the terrain following maneuver are shown in Figure 5.13. The vehicle response to this input can be seen in Figures 5.14 through 5.16. Similar to the batch results, the short term damage reduction was insignificant. Starting with a 2 millimeter crack yielded a crack growth of less than 0.001 mm during the entire maneuver for both cases shown in Figure 5.17. However, as the crack length grows, the crack growth rate per cycle grows as well according to Newman’s crack growth model. Over time, this will increase the crack growth rate until the component breaks.

This was simulated by repeating the same maneuver many times. The aggressive maneuver from

Figure 5.17 was repeated 5,000 times, representative of damage accumulation over the life of 57 the component. When the DMC was off, the crack length doubled after 3,500 maneuvers and tripled after 4,500 maneuers. With DMC engaged, the crack grew less than 1 mm over the 5,000 maneuvers span. These results are shown in Figure 5.18.

Figure 5.13. Utility Helicopter Stick Inputs for the Piloted Pitch Doublet Maneuver 58

Figure 5.14. Utility Helicopter Attitudes for Piloted Pitch Doublet Maneuver 59

Figure 5.15. Utility Helicopter Rates for Piloted Pitch Doublet Maneuver 60

Figure 5.16. Utility Helicopter Response for Piloted Pitch Doublet Maneuver

Figure 5.17. Utility Helicopter Load and Damage Results for Pitch Doublet Maneuver 61

Figure 5.18. Utility Helicopter Crack Length Growth Over Lifetime for Pitch Doublet Maneuver

The roll axis was also investigated using a piloted roll reversal maneuver. Beginning in trimmed flight at 120 knots, the helicopter was banked left approximately 45 degrees. After several seconds in the steady turn, a hard right roll was performed. The control inputs for this maneuver are shown in Figure 5.19. The attitude and rate responses are in Figures 5.20 and 5.21, respectively. Both figures show effects of the damage mitigation control. During the roll right, the roll attitude increased at a constant rate with DMC engaged. This caused the maneuver to take an additional two seconds. Much like the pitch maneuver, a single roll reversal does not cause the crack length to grow by a significant ammount. Figure 5.22 shows this negligible crack growth. Again, the long term effects are more prominent after repeating the maneuver 5,000 times. Though not as significant as the pitch maneuver, the repeated roll reversals cause the crack to grow an additional 0.4 mm without DMC and only 0.14 mm with DMC. Note that these results contradict the batch simulation results, where the roll maneuver was shown to cause more damage to the pitch link. One possible explanation is that during the batch simulations, all but one inputs are constant, so the off axis responses are small. During the piloted simulations, all inputs were controlled, so the off axis responses were larger. This could have compounded the damage during the piloted pitch maneuver, causing the crack to grow much quicker. 62

Figure 5.19. Utility Helicopter Stick Inputs for the Piloted Roll Doublet Maneuver 63

Figure 5.20. Utility Helicopter Attitudes for Piloted Roll Doublet Maneuver 64

Figure 5.21. Utility Helicopter Rates for Piloted Roll Doublet Maneuver

Figure 5.22. Utility Helicopter Load and Damage Results for Roll Doublet Maneuver 65

Figure 5.23. Utility Helicopter Crack Length Growth Over Lifetime for Roll Doublet Maneuver 66

5.3.2 Handling Qualities

The handling qualities for the utility helicopter were assessed using the ADS-33 requirements for small and moderate amplitude changes in forward flight. To get the small amplitude requirement, a frequency sweep was conducted and the bandwidth and phase delay were calculated as defined in Equation 5.1 and Figure 5.24. Figure 5.24 is a sample frequency response for the utility helicopter without DMC. For the moderate amplitude changes, simulations were run to gather the peak attitude and rate chage as well as the minimum attitude change. An example is shown in Figures 5.25 and 5.26. The bandwidth and phase delay specifications for pitch are shown in Figure 5.27. The small amplitude bandwidth and phase delay specifications for the roll axis are in Figure 5.28. Both figures show no degradation in handling qualities for small amplitude changes. Small lateral inputs show no difference with DMC on or off while the small longitudinal inputs show a slight change. All handling qualities for small amplitude changes remained well within the level 1 region.

∆Φ2ω180 τp = (5.1) 57.3(2ω180)

Figure 5.24. Definitions of Bandwidth and Phase Delay Using Roll Attitude due to Lateral Cyclic as an Example 67

Figure 5.25. Definitions of ∆φpk and ∆φmin for Moderate Amplitude Change

Figure 5.26. Definition of Ppk for Moderate Amplitude Change 68

Figure 5.27. Requirement for Small Amplitude Pitch Attitude Change at 120 knots Forward Flight for Utility Helicopter

Figure 5.28. Requirement for Small Amplitude Roll Attitude Change at 120 knots Forward Flight for Utility Helicopter 69

The moderate amplitude pitch change is shown in Figure 5.29. Here, the case without DMC is clearly in the level 1 region for all moderate pitch changes in forward flight. When the DMC is on, the handling qualities degrade much quicker, however they remain in the level 1 region. If the curve is extrapolated past the known data points, it is possible that the handling qualities will dip below the boundary into the level 2 region. Although not ideal, this is acceptable as only extremely aggressive pitch maneuvers would cause the handling qualities to degrade to level 2.

For most flight maneuvers, the vehicle would remain in the level 1 handling qualities region.

The moderate amplitude roll change showed no degradation to the handling qualities. Figure

5.30 shows that there is only a slight difference between the two cases, yet they both remain definitively in level 1.

Figure 5.29. Requirement for Moderate Amplitude Pitch Attitude Change at 120 knots Forward Flight for Utility Helicopter 70

Figure 5.30. Requirement for Moderate Amplitude Roll Attitude Change at 120 knots Forward Flight for Utility Helicopter

5.4 Heavy-Lift Transport Helicopter Simulation

Three components on the heavy-lift transport helicopter were studied. These three components were the pitch link, the main rotor shaft, and the stationary scissors. For each component, a loads model and a damage model was provided by TDA, which was used to analyze the effectiveness of damage mitigation control through batch and piloted simulations.

5.4.1 Loads and Damage Reduction

It was previously established that maneuvers that caused a high load factor and high pitch acceleration produced the largest loads, so the pitch axis was the focus of the heavy-lift transport helicopter damage mitigation research.

5.4.1.1 Batch Simulations

For the batch simulations, the control inputs are shown in Figure 5.31. The longitudinal stick was pushed forward to -20% at a rate of 50% per second and held there for five seconds. The longitudinal stick was then pulled back to +20% at the same rate. After five more seconds, the 71 stick was returned to the trimmed position. Figures 5.32 through 5.34 show the vehicle response to this maneuver. The pitch attitude is strongly affected by the damage mitigation control, as evidenced by Figure 5.32. During the aggressive pull-up, the pitch attitude quickly increased from -12 degrees to +11 degrees when the DMC was not used. The pitch rate limit is clearly seen when DMC was used, causing the aggressive pitch maneuver to steadily increase the pitch attitude. The pitch attitude increased at a rate of 4.5 deg/sec, as evidenced by Figure 5.33. In the case without DMC, the pitch rate quickly increased to 24 deg/sec during the pull-up and then returned to zero until the stick was returned to trim.

Figure 5.31. Heavy-Lift Transport Helicopter Control Inputs for Batch Pitch Doublet Maneuver 72

Figure 5.32. Heavy-Lift Transport Helicopter Attitude Response for Batch Pitch Doublet Maneuver 73

Figure 5.33. Heavy-Lift Transport Helicopter Rate Response for Batch Pitch Doublet Maneuver 74

The effect on the airspeed and load factor is shown in Figure 5.34. The airspeed increases indentically until the pull-up maneuver. Once the pull-up begins, the case without DMC slows down much quicker than the case with DMC. When DMC was used, the vehicle continued to increase in airspeed for about two extra seconds until it began to slow down. The load factor is shown to reduce from a maximum 2 g’s to about 1.5 g’s. The next section will discuss the piloted simulations.

The batch simulations showed benefits of using damage mitigation control. All three compo- nents (pitch links, rotor shaft, and stationary scissors) exhibited a reduction in loads and damage when DMC was used. The plots could not be shown however, as some of the data is not available in the public domain.

Figure 5.34. Heavy-Lift Transport Helicopter Response for Batch Pitch Doublet Maneuver 75

5.4.1.2 Piloted Simulations

The piloted simulations for the heavy-lift transport helicopter used the same terrain following manuever as the utility helicopter. The pilot control inputs to this maneuver are in Figure 5.35.

The vehicle response can be seen in Figures 5.36 through 5.38, which shows the vehicle attitudes, rates, and load factor and airspeed, respectively.

The attitudes in Figure 5.36 show similar results to those seen in the batch simulations. The

DMC causes the pitch rate to gradually increase during the aggressive maneuver as opposed to the sudden jump caused without using DMC. The roll attitude remained low and the yaw attitude increased slowly, averaging +1 deg/sec.

The rate responses in Figure 5.37 also match what was seen in the batch simulations. Although the main difference here is that there were more oscillations without DMC. These were most likely due to the pilot making slight adjustments to the controls throughout the maneuver. As evidenced by the pitch rate plot and noted by the pilot, the DMC reduced the oscillations significantly as the extreme maneuver reduced the maximum pitch rate from 25 deg/sec to 15 deg/sec.

The airspeed and load factor are shown in Figure 5.38 and show the significant reduction in load factor due to the damage mitigation control. The peak load factor without DMC is about

2.5 g’s, while the limiter reduces the maximum load factor to 1.8 g’s.

The damage mitigation controller showed good results with a reduction to the loads and damage for all three components, similar to what was seen in the batch simulations. Again though, the damage reduction plots could not be presented as they contain data not available in the public domain. 76

Figure 5.35. Heavy-Lift Transport Helicopter Stick Inputs for Piloted Pitch Doublet Maneuver 77

Figure 5.36. Heavy-Lift Transport Helicopter Attitude Response for Piloted Pitch Doublet Maneuver 78

Figure 5.37. Heavy-Lift Transport Helicopter Rate Response for Piloted Pitch Doublet Maneuver 79

Figure 5.38. Heavy-Lift Transport Helicopter Response for Piloted Pitch Doublet Maneuver 80

5.4.2 Handling Qualities

The handling qualities were assessed for roll and pitch quickness and in forward flight. Figures

5.39 and 5.40 show that the heavy-lift transport helicopter model meets level 1 handling qualities for small amplitude pitch and roll changes. There is no degradation in small amplitude handling qualities when the DMC in engaged. This was expected as the limiters were not triggered during these small amplitude oscillations.

The moderate amplitude pitch changes in forward flight did show a degradation of handling qualities. Figure 5.41 shows the comparison of moderate amplitude pitch changes with and without DMC. The handling qualities without DMC are well in the level 1 region. When DMC is engaged, the handling qualities degrade sharply, however they still remain level 1 for a majority of pitch maneuvers. It is only during the extremely aggressive pitch maneuvers that the vehicle drops into the level 2 region. This is the same situation seen with the utility helicopter.

Figure 5.39. Requirement for Small Amplitude Roll Attitude Change in Forward Flight for Heavy-Lift Transport Helicopter 81

Figure 5.40. Requirement for Small Amplitude Pitch Attitude Change in Forward Flight for Heavy-Lift Transport Helicopter

Figure 5.41. Requirement for Moderate Amplitude Pitch Attitude Change in Forward Flight for Heavy- Lift Transport Helicopter Chapter 6

Conclusions and Future Work

A linear dynamic inversion controller was designed to reduce the fatigue loads experienced by several crucial components in the rotor hub and the controller was tested on two separate heli- copters. One helicopter was a utility helicopter similar to a UH-60 and the other was a heavy-lift transport helicopter similar to a CH-53E. The controller implemented rate limiters in the roll and pitch command filters to reduce the high fatigue loads experienced by the components in question. A former Marine helicopter pilot flew the piloted simulations and provided feedback on the qualitative handling qualities of the helicopters.

Simulations showed that using rate limiting control as a means of damage reduction was effective during aggressive maneuvers at high airspeeds. Using a crack growth damage model for the pitch links, damage mitigation control more than tripled the life of the pitch link when performing aggressive pitch maneuvers. When performing aggressive roll maneuvers, the life of the pitch link increased by a factor of two, with the potential to increase more due to the non-linearity of the lifetime damage.

Using component S-N curves to construct a damage model for each component showed a reduction to the component fatigue loads while maintaining acceptable handling qualities for the heavy-lift transport helicopter. During aggressive pitch maneuvers, the damage to the pitch links, rotor shaft, and stationary scissors was reduced. The only degradation to handling qualities to note was that very large pitch maneuvers caused the moderate amplitude pitch change handling qualities to degrade to the level 2 region.

Several steps could be taken to improve the effectiveness of the controller. By implementing 83 a HUMS in conjuction with the damage mitigation controller, the helicopter could automatically toggle the DMC on or off depending on the current life of the components. This would allow the helicopter to “self assess” and determine when damage mitigation control was necessary. Another method to further the research of DMC would be to implement a tactile feedback cueing system.

In doing so, the pilot would be notified when a limit was reached, encouraging him/her to reduce the force applied to the stick. However, the pilot would be able to ignore or override the limiter if they were in a life-threatening situation.

Damage reduction through load alleviating control is a promising area of research for rotor- craft. As fly-by-wire control systems are utilized in next generation aircraft, control systems can be designed to increase component fatigue life and reduce maintenance costs while maintaining good handling qualities. Appendix

CSGE Diagrams

Figure A.1. Longitudinal Actuator Control

Figure A.2. Lateral Actuator Control 85

Figure A.3. Collective Actuator Control

Figure A.4. Pedal Actuator Control 86

Figure A.5. Dynamic Inversion Control Architecture 87

Figure A.6. Pitch Axis Compensator

Figure A.7. Pitch Axis Command Filter 88

Figure A.8. Pitch Axis Limiter

Figure A.9. Roll Axis Compensator

Figure A.10. Roll Axis Command Filter 89

Figure A.11. Roll Axis Limiter 90

Figure A.12. Dynamic Inversion Block 91

Figure A.13. Logic for Limiter Switch References

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