# EMEA. Rebecca Margetts Senior Engineer: Mathematical Modelling AgustaWestland. Development of a Helicopter Drivetrain Dynamics Model in MSC ADAMS

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1 EMEA Rebecca Margetts Senior Engineer: Mathematical Modelling AgustaWestland Development of a Helicopter Drivetrain Dynamics Model in MSC ADAMS

2 Introduction The AW101 Helicopter The Task Theory Existing Models Method Crawl - Walk - Run Or Drivetrain - Local Installation - Full Aircraft Results & Discussion Conclusions & Further Work Presentation Outline

3 Introduction: Purpose Development of AW101 (aka. EH101 or Merlin ) Medium/Heavy Lift 3 Engines 5 Main Rotor Blades Utility, Maritime and SAR variants In-Flight vibration levels indicate a mode of the Main Rotor Gearbox Rigid body yawing, flexible bending, or a coupled mode? Future aircraft modifications could alter this mode. Understanding this mode could reduce vibration levels Extend component life. Increase passenger comfort. NB: We refer to the Blade Passing frequency as 5R

4 Ground Shake Test: No modes in range Simple ADAMS model: Gearbox Yaw Mode above 5R Flight Data + Engineering Judgement: Gearbox Yawing Modes above & below normal 5R 6 Indicative of mode above 'normal' 5R 5 4 5R Vibration Higher than expected response at low rotor speed => mode below 'normal' 5R Impact Testing: Gearbox Yaw Mode above 5R Detailed ADAMS Model including Drivetrain FE Model: Gearbox Yaw mode above 5R 0 Rotor Speed Preliminary Operational Modal Analysis: possible yawing modes around 5R

5 Introduction: Task Statement There is a Mode below 5R that Impact/Modal Tests and Finite Element modeling do not predict. This could be due to a transmission mode coupling with the system Hence the mode is only seen in flight It is hypothesized that the 2 nd lag mode of the main rotor blades is coupling: similar frequency. This mode must be understood, in order to control the vibration Proposed modifications to the aircraft could alter the frequency of this mode: moving it closer to 5R could potentially increase vibration. We can pinpoint and trial vibration reduction methods in a virtual environment.

6 Introduction: How has this been tackled in the past? Drivetrain dynamics were historically analysed in isolation Hand calculations on simplified coupled systems Engineering judgment was used to estimate coupling. Other systems have been coupled in FORTRAN Aircraft stability, Coupled Rotor-Fuselage model

7 Background: Modal Coupling Theory z P? l 1 Engine Mounts l 2 m, I k 1 k 2 Engine Coupling Terms Modes are associated with a motion, e.g. vertical, roll. They can couple to give responses with out of plane components. Due to non-coincident axes, non-linearities in the system, etc. E.g. an Engine with an offset centre of gravity. Looking at the Roll degree of freedom: 2 2? ml z? k ( l? l ) z? ( I? ml )?? k ( l? l )? ? In multi-body systems, components also interact with each other. E.g. a fuselage bending mode will include terms relating to motions of mounted equipment. 0

8 Background: Transmission (Detailed) A Gearbox can be modeled well in MSC ADAMS. E.g. this accessory gearbox (pictured) For this task we need the whole drivetrain (including Main Rotor Gearbox, Accessory Gearbox, 3x Reduction Gearboxes, Intermediate and Tail Rotor Gearboxes, Engines and Rotors) This is a huge task to model in detail Time consuming Prone to cumulative geometric / human errors

9 Background: Transmission (Simplified) Holzer-Myklestadt Method is used to simplify the drivetrain branches of point inertias and torsional springs. Elements are set to rotate at the same speed by factoring in the gear ratio n Historically Holzer-Myklestadt was used to model transmissions in Matlab or MSC Nastran Only gives rotational modes J1 J1 k1 k1 J3 J2 k2 n 2 k2 J4 J4 J2 + n 2 J3

10 Background: Transmission (Nastran) Schematic Visualised in MSC Patran

11 The Drivetrain must be Geometrically Correct in order to couple correctly We cannot just import the Holzer- Myklestadt model from Nastran Coupling Statements can be used to connect drivetrain components Method: Drivetrain Model This removes the necessity to factor in the gear ratios However, dummy parts must be used, otherwise the coupling statements will override the torsional springs Structural Damping Complex Stiffness cannot be input Frequency-Dependent Elements & Transfer Functions were problematic had to use trial-and-error. Equivalent Viscous Damping Used c? 2?? eq n

12 Method: Main Rotor Blade Modelling Hub Blade Representation Main Rotor Blade Our hypothesis is that the 2 nd lag mode of the main rotor blades is coupling. We shall neglect the flap and torsion modes here Although they could be included in future models AW101 has a fully articulated rotor For the 1 st lag mode, we can consider the blades to be rigid, as most bending occurs at the hinge For the 2 nd lag mode, we can extend this assumption We know the hub properties, and the modal frequencies of the first and second lag modes Therefore we can define equivalent point inertias and torsional springs.

13 Method: Adding Drivetrain to Gearbox Model The inertias are mounted to the casings with revolute joints These are essentially perfect bearings: no rotational stiffness (and no stiffness coupling)

14 Method: Adding Fuselage to Model It is known that some of the modes are a results of cabin roof flexibility A fuselage body was produced from the Nastran model of the aircraft, and a flexible body was created using ADAMSMNF This *.mnf file was imported into ADAMS using ADAMS/Flex The bushings representing the main rotor gearbox feet and engine mounts were attached to the fuselage. The fuselage was fixed to the ground at the centre of gravity.

15 Results: Free-Free Undamped Drivetrain Modes The Drivetrain Modes were compared to those gained using Holzer-Myklestadt method (computed in Matlab) They correlated well. These frequencies are used to calculate equivalent viscous damping for the drivetrain system

16 Results: Drivetrain & Main Rotor Gearbox Models Merged FRF (No Damping) (Rad / N-mms) 5R An actuator input is specified at the main rotor hub, applying 1Nm about the vertical axis. Angular velocity is output at the main rotor hub, about the vertical axis. A Swept Sine Forced Response analysis is used. The Frequency Response Function is therefore the point Mobility or Mechanical Admittance of the system.

17 A Mode occurs below 5R, as anticipated. This mode results in a yawing motion of the installation. Inspecting the Modal Energy tables confirms that this is the 2nd lag mode of the blades. Results: Drivetrain & Main Rotor Gearbox Models Merged FRF (No Damping) (Rad / N-mms) The Yawing mode above 5R is still present. Inspecting the Modal Energy tables shows that this is a fore/aft mode of the outer engines. An actuator input is specified at the main rotor hub, applying 1Nm about the vertical axis. Angular velocity is output at the main rotor hub, about the vertical axis. A Swept Sine Forced Response analysis is used. The Frequency Response Function is therefore the point Mobility or Mechanical Admittance of the system.

18 Results: Evidence of Coupling on Drivetrain & Main Rotor Gearbox Installation The Mass, Stiffness and Damping matrices can be output using ADAMS/Linear The Mass and Stiffness matrices show coupling terms as off-diagonal terms. Each row and column refer to a part s degree of freedom Hence we can identify the coupling between, for example, an engine internal and outer part.

19 Results: Complete Aircraft FRF (No Damping) (Rad / N-mm-s) 5R The inset shows responses above and below 5R

20 Results: Animation of Mode Below 5R There is a mode close to 5R, containing some yaw motion. Inspecting the Animation and Modal Energy tables confirms that this is the 2nd lag mode of the blades.

21 Results: Animation of Mode Above 5R There is also a mode well above 5R, which is a MRGB yaw and fuselage torsion mode.

22 Results: Complete Aircraft FRF (With Damping) (Rad / N-mm-s) 5R There is a small response at almost exactly 5R The mode above 5R is still present

23 Discussion Drivetrain only model The normal modes correlate well to those gained using Holzer- Myklestadt Method. Coupled Main Rotor Gearbox and Drivetrain Model The normal modes identify a yawing of the Main Rotor Gearbox below 5R, as hypothesised. The normal mode above 5R is also identified. Full Model (Including Flexible Fuselage) The normal modes and undamped Forced Response revealed responses above and below 5R, as hypothesised. The damped Forced Response showed that the blade passing frequency coincides with a small response. Not all modes respond when damped. Altering the blade, fuselage and/or main rotor gearbox mounting structure could potentially improve or worsen the vibration environment.

24 Conclusions We can successfully couple two systems in ADAMS We can use this technique to predict the effects of proposed changes to the Main Rotor Blades and Gearbox with confidence.

25 Further Work Could this have been done in MSC Nastran? Problematic: Geometry must be taken into account when specifying MPC and CBUSH terms in Nastran, known grounding problems using CELASi. The Forced Response analysis requires significant manipulation of the Bulk Data File in Nastran. ADAMS/Vibration is more intuitive. In Nastran, a preliminary full model often took over an hour to run. In ADAMS/Vibration it takes under a minute. The transfer function for the aircraft without the blades can be obtained and used in a FORTRAN whole aircraft model The Rotor Systems Group have detailed FORTRAN Main Rotor models. Long term: there is currently research into compiling full aircraft models in ADAMS Aircraft Stability, Deck Operations, Undercarriage behavior.

26 Acknowledgements & References Mr A. Vincent, AgustaWestland Dr S. King, AgustaWestland Mathematical Modelling, AgustaWestland Bielawa, R. L., Rotary Wing Structural Dynamics and Aerolelasticity, 2nd Edition, AIAA, 2006

27 EMEA For further information please contact Rebecca Margetts MEng(Hons) CEng MIMechE Senior Engineer: Mathematical Modelling AgustaWestland, Yeovil, UK. This information is copyright AgustaWestland 2007

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