Hover Flight Helicopter Modelling and Vibrations Analysis

Transcription

1 ISBN Comité Español de Automática de la IFAC (CEA-IFAC) 473 Hover Flight Helicopter Modelling and Vibrations Analysis Salvador Castillo-Rivera The School of Engineering and Mathematical Sciences. The City University London. United Kingdom, M. Tomas-Rodriguez The School of Engineering and Mathematical Sciences. The City University London. United Kingdom, Abstract In this work, different modelling aspects of helicopter aerodynamics are discussed. The helicopter model is on Sikorsky configuration, main rotor in perpendicular combination with a tail rotor. The rotors are articulated and their blades are rigid. The main rotor implementation takes into account flap, lag and feather degrees of freedom for each of the equispaced blades as well as their dynamic couplings. The model was built by using VehicleSim, software specialized in modelling mechanical systems composed by rigid bodies. Appearing vibrations due to the rotating behaviour of the rotors are studied in here. This work presents an aerodynamic model that allows to simulate hover flight. The aerodynamic model has been built up using blade element theory. The aerodynamic load creates vibrations on the helicopter and these are analyzed on the fuselage by using short time Fourier transform processing to study the vibrations spectrum. The results of the simulations are presented and compared to existing mechanical vibrations generated by a dynamic model developed by the authors as well as existing theory in the specialist literature. Keywords: Vibrations, helicopter, dynamics, aerodynamics. 1 INTRODUCTION Helicopter vibration is common a problem which involves complex interactions between the inertial, structural loads and aerodynamic loads. The major source of vibrations in helicopters is the main rotor, whereas in fixed-wing aircraft, the vibrations are mostly originated by the engines or are caused by atmospheric turbulences. In aircraft's design, vibrations have remained one of the major problems affecting helicopter development for years. In fact, the maximum speed and manoeuvring capabilities for most of the modern helicopters are limited by excessive vibration. Vibrations frequencies are either equal to the rotors frequencies or multiple of them. The rotors frequencies are a function of the angular speeds at which they rotate [5]. Vibrations affect ride comfort, adds to the fatigue of pilots, crew, and passengers and increases maintenance time and cost. High vibration levels experienced by a helicopter could in many cases pose a limitation to the vehicle s forward speed and manoeuvring capabilities. In addition to this, vibrations affect the helicopter handling qualities, contribute to the fatigue of structural components, reduce the reliability of on board electronic equipment, and influence the precision of equipment such as cameras, measure devices, etc. [7], [11]. The reduction of helicopter vibrations has traditionally been a difficult task to achieve. Vibrations should be analysed and study in order to identify their main frequencies. This information can be used to design vibration control methods for helicopters [8]. The structure of the article is as follows: in sections 2 and 3, the aspects of the dynamic helicopter model are considered. Section 4 describes VehicleSim environment, used to implement the model of the helicopter. In section 5, a hover aerodynamic model is provided. Vibrations analysis on the fuselage, as a consequence of the aerodynamic and dynamic loads are given in Section 6. Section 7 contains the conclusions of the article. 2 DYNAMIC MODEL The helicopter under study is on Sikorsky configuration i.e., main rotor in perpendicular combination with a tail rotor. Both systems are mounted on the fuselage. The helicopter model consists of fuselage, main rotor and tail rotor, both articulated. The main rotor consists of four equally spaced blades joined to a central hub and the tail rotor consists of two equally spaced blades joined to a secondary hub. The blades are rigid in both rotors.

2 ISBN Comité Español de Automática de la IFAC (CEA-IFAC) 474 The helicopter has six degrees of freedom: three translations along the (X, Y, Z) axes and three rotations around the same axes. The model presented in this paper is based in previous works developed by the authors (see [2], [3], [4], [10], [14]). 2.1 FUSELAGE The fuselage is the rotorcraft's main body section that holds crew and passengers, amongst other. Its degrees of freedom are the lateral and longitudinal translation in the horizontal plane X-Y axis, vertical translation (Z axis) and rotation about these same axes corresponding to yaw, pitch and roll. 2.2 MAIN ROTOR The role of the main rotor is to support the aircraft's weight, as it generates the lift force. It allows to keep the helicopter suspended in the air and provides the control that allows to follow a prescribed trajectory in the various spatial directions by changing altitude and executing turns. It transfers prevailingly aerodynamic forces and moments from the rotating blades to the non-rotating frame (fuselage). The blades are kept in uniform rotational motion (rotational speed ), by a shaft torque from the engine. A common design solution adopted in the development of the helicopter is to use hinges at the blades roots that allow free motion of the blade normal to and in the plane of the disc. The most common of these hinges is the flap hinge which allows the blade to flap, this is, to move in a plane containing the blade and the shaft, of the disc plane, about either the actual flap hinge or in some other cases, the flap hinge is substituted by a region of structural flexibility at the root of the blade. The flap hinge is more frequently designed to be a short distance from the centre line. This is termed an "offset" (er), and it offers the designer a number of important advantages. A blade which is free to flap, experiences large Coriolis moments in the plane of rotation and a further hinge (called lag) is provided to relieve these moments. This degree of freedom produces blade motion on the same plane as the disc. In presence of aerodynamic loads this degree of freedom generates the blade s drag force. A blade can also feather around an axis parallel to the blade span. Blade feather motions are necessary to control the aerodynamic lift developed and, in forward motion of the helicopter, to allow the advancing blade to have a lower angle of incidence than the retreating blade and thereby to balance the lift across the craft. In order to be able to climb up, the feather angle needs to be increased. On the other hand, in order to descend, the blade's feather angle is decreased. Because all blades are acting simultaneously in this case, or collectively, this is known as collective feather and allows the rotorcraft to rise/fall vertically. Additionally to this control, for achieving forward, backward and sideways flight, a different additional change of feather is required. The feather on each individual blade is increased at the same selected point on its circular pathway. This is known as cyclic feather or cyclic control. Blade feather control is achieved through linkage of the blade to a swashplate. 2.3 TAIL ROTOR The tail rotor is mounted in perpendicular to the main rotor. It counteracts the torque and the yaw motion that the main rotor disc naturally produces. In accordance to Newton's third law of action and reaction, the fuselage tends to rotate on the opposite direction to the main rotor's blades as a reaction of the torque that appears (see Figure 1). Figure 1: Tail rotor counteracting the torque induced by the main rotor rotation. This torque must be counteracted and/or controlled before any type of flight is possible. Two anti-torque pedals allow the pilot to compensate for torque variance by providing a means of changing pitch (angle of attack) of the tail rotor blades. This provides heading and directional control in hover and at low airspeeds. Driven by the main rotor at a constant ratio, the tail rotor produces thrust in a horizontal plane opposite to torque reaction developed by the main rotor. Since the main rotor torque varies during flight when power changes are made, it is necessary to vary the thrust of the tail rotor. A significant part of the engine power is required to drive the tail rotor, especially during operations when maximum power is used. Any change in engine power output produces a change in the torque effect.

3 ISBN Comité Español de Automática de la IFAC (CEA-IFAC) VEHICLESIM AS MODELLING TOOL VehicleSim is a multibody modelling software. It has been used over a wide range of mechanical dynamic studies, mainly in connection to vehicle dynamics [13] and it has provided the basis for commercial simulation codes such as TruckSim, CarSim and BikeSim [6]. The syntactic rules of VehicleSim are straightforward. The output from VehicleSim can take one of several forms: (a) a rich text format file containing the symbolic equations of motion of the system described; (b) a C language simulation program with appropriate data files containing parameter values and simulation run control parameters or (c) linear state space equations in a MATLAB M file format that contains symbolic state space A, B, C, D matrices that can be used for linear analysis. Once the model has been built, it becomes independent of VehicleSim and can be executed at any time. 4 PROGRAM STRUCTURE VehicleSim Lisp is used to develop the multibody system code that represents a helicopter system. The multibody system is subdivided into its constituent bodies for the purpose of writing the VehicleSim code. The bodies are arranged as a parent-child relationship. The first body is the inertial frame and it has the fuselage as its only child. The fuselage is located at the origin of the inertial coordinates system and it is the parent of both the main and tail rotors. The main rotor rotates around its vertical axis, Z axis. The main rotor is the parent of the flap hinge that rotates around the corresponding X axis, the lag hinge is the child of the flap hinge. The lag hinge rotates around the Z axis. The feather hinge is the child of the lag hinge. The feather hinge rotates around the Y axis. Finally, the blade is added to the program structure as the child of the feather hinge. The tail rotor is built up following this same parentchild structure. Table 1: Parameter s values. Parameters Symbol Value Helicopter Mass m h 2064 (kg) Blade one mass m bl (kg) Blade two mass m bl (kg) Blade three mass m bl (kg) Blade four mass m bl (kg) Spring flap hinge k fj (Nm/rad) Spring lag hinge k lj (Nm/rad) Damping lag hinge d lj (Nms/rad) Main Rotor Speed Ω 44.4 (rad/s) 5 AERODYNAMIC MODEL IN HOVER 5.1 AIR DENSITY For every flight condition, the air density changes with the height (h), for the lower atmosphere where helicopters fly below 6000 m, the standard value of air density can be approximated as: where h is expressed in meters and ρo is kg/m 3 (air density at sea level) [9]. 5.2 INDUCED HOVER SPEED In hovering flight, the induced velocity can be obtained as v i = v io, v io is the hover induced velocity, which can be considered constant in hover, the traction force, T, becomes equal to the disc loading (weight of the helicopter), see Figure 2 [9]: 4.1 DYNAMIC MODEL DESCRIPTION The parameters used for the dynamic simulation carried out in this work are shown in table 1 ([14]). For the purpose of dynamical modelling only, the action of external forces not considered, for example: gravity. The system can be considered in the vacuum. An unbalance of masses is considered on the main and the tail rotors blades in order to simulate a source of vibrations in the helicopter with an amplitude to be detected in the spectrum. On the other hand, in order to simulate the engine effects on each rotor, the main and tail rotors angular speeds are modelled using PID controllers. Figure 2: Main forces acting on a helicopter in hover flight.

4 ISBN Comité Español de Automática de la IFAC (CEA-IFAC) BLADE ELEMENT ANALYSIS IN HOVER FLIGHT Blade element theory forms the basis of most modern analyses in helicopter rotor aerodynamics as it estimates the radial and azimuthal distributions of blade aerodynamic forces (and moments). In addition to this, the rotor performance can be obtained by integrating the sectional airloads at each blade's elements over the length of the blade and averaging the result over a rotor revolution [9]. Figure 3 is a plan view of the rotor disc, viewed from above. The blade radius is R and the tip speed is given by ΩR. An elementary blade section is considered at radius y, of chord length c and spanwise width dy. Figure 4: Velocity components U T and U p. If the feather angle at the blade element is θ, then the aerodynamic or effective angle of attack is: The resultant incremental lift, dl, and drag dd per unit span on a blade element are: where ρ is the air density, C l and C d are the lift and drag coefficients, c is the local blade chord. The lift dl and drag dd act perpendicular and parallel respectively to the resultant flow velocity. Figure 3: Main rotor disc viewed from above. The velocity components on the blade's section are shown in Figure 4. The flow seen by the section has velocity components Ωy in the disc plane and (v i + V c ) (v i is the induced velocity and V c is the upward velocity) perpendicular to it [12]. The resultant local flow velocity at any blade element at a radial distance y from the rotational axis has an out of plane component U p = (v i +V c ) normal to the rotor plane as a result of climb and induced inflow and an in plane component U T = Ωy parallel to the rotor due to blade rotation, relative to the disc plane. The resultant velocity at the blade element is therefore the composition of both [9]: 5.4 THRUST COEFFICIENT The thrust coefficient approximation for hover flight can be written as: θ is the feather angle, a is the lift slope, λ = v ih /ΩR, v ih is the induced hover velocity, R is the rotor radius and σ is the solidity factor which for a constant blade chord is given by: The blade s feather angle θ, is imposed by the pilot's collective control input. The angle between the flow direction and the plane of rotation, known as the inflow angle ϕ, is therefore [12]: N is the number of main rotor blades and c is the blade chord [12]. 6 VIBRATIONS ANALYSIS The analysis of the vibration modes on a helicopter is a difficult task due to the complexity of the structure,

5 ISBN Comité Español de Automática de la IFAC (CEA-IFAC) 477 but reasonable accuracy is achievable with modern techniques. This work is carried out by estimating the vibrations appearing in hover flight when the aerodynamical model has been implemented as well as a comparison to dynamic vibrations generated under the excitation conditions described previously. In order to develop the proposed analysis, it is necessary to follow the next steps: a) detection of vibration signals on the fuselage as a consequence of the hover aerodynamic load and with unbalance of masses, separately b) analysis of the spectrogram for identification of the detected vibrations. 6.1 VIBRATIONS IN HOVER FLIGHT Figure 5: Vibrations on the fuselage's X axis for hover flight. In here, the vibrations appearing on the fuselage's axes X (roll) and Y (pitch) during hover flight are studied. Only two axes are analysed as these are enough to validate the expected behaviour. It is known that vibrations are generally low in hover flight [7]. The aerodynamic model satisfies the following structural characteristics: the flap and lag degrees of freedom do not have springs fitted although the lag maintains a damper. In addition to this, it does not exist an unbalance of masses on the main and tail rotors. There is a consequence of the use of a rotating frame of reference that affects vibration frequencies created in the rotor and transmitted to the fuselage. The frequencies generated in the rotor may contain the rotational frequency of the rotor and the external perturbation frequency [15]. In order to analyze the vibrations appearing on the fuselage, the Short Time Fourier Transform (STFT) is used. A hover flight simulation is done; the simulations are carried out for 50 seconds, although the results plotted in figures 5, 7, 9 and 11 show the first 5 seconds only, for clarity of the view. The height is h = 250 m and the main rotor's collective feather angle is rad and tail rotor's collective feather angle is also rad. Figure 5, shows the fuselage's oscillations (vibrations) on the X axis during hover flight for 5 seconds. Figure 6, shows the corresponding spectrogram obtained for this simulation. Various predominant frequencies which come from the main rotor loads (approximately 7.6 Hz) can be seen, this is the flap frequency. There is a second predominant frequency (approximately 15.2 Hz) this is twice the flap frequency and a third predominant frequency is found at around 37.1 Hz, this frequency coincides with the tail rotor blades flap frequency. Figure 6: Fuselage's X axis spectrogram in hover flight conditions. Similar analysis is carried out for the oscillations appearing on the fuselage's Y axis (see Figure 7). The three predominant frequencies of these vibrations appear in the spectrogram in Figure 8. These are approximately 7.6 Hz which are caused by the main rotor blades flap, the second frequency is approximately 15.2 Hz, this value is twice the main rotor flap frequency and the third frequency is around 37.1 Hz, it is associated to the tail rotor flap motion. Figure 7: Vibrations on the fuselage's Y axis for hover flight.

6 ISBN Comité Español de Automática de la IFAC (CEA-IFAC) 478 presented in this case), the oscillation on the fuselage's X axis shows two predominant frequencies which are originated at the main rotor (7 Hz approximately) and at the tail rotor, in this case, the value is around of 37 Hz. Figure 8: Fuselage's Y axis spectrogram in hover flight. 6.2 DYNAMIC VIBRATIONS In this section, the vibrations when both flap and lag modes are coupled will be studied when the main and tail rotor have a constant angular speed. In this case, the vibrations are introduced in the model by unbalance of masses in both rotors; the mass of the blades on the main rotor are mbl 1 = kg, mbl 2 = kg, mbl 3 = kg and mbl 4 = kg and on the tail rotor they are; mbltl 1 = kg and mbltl 2 = kg. The collective and cyclic feather angles are zero in the main rotor. The tail rotor flap dynamics are modelled as a Fourier series: β tl =a o - a 1 cos(ωt) -b 1 sin(ωt) where a o = 0.01 rad, a 1 = 0.01 rad and b 1 = 0.01 rad are the corresponding coefficients, and the collective angle is 0.01 rad. The main rotor angular speed is constant at 44.4 rad/s. Figure 9, shows the fuselage's oscillations (vibrations) around the X axis under the previous conditions. Figure 10: Fuselage vibrations spectrogram on the X axis for mbl 1 = kg, mbl 2 = kg, mbl 3 = kg and mbl 4 = kg and on the tail rotor they are; mbltl 1 = kg and mbltl 2 = kg. Similar analysis can be carried out for the spectrogram of frequencies in fuselage s Y axis (see figures 11 and 12). Two predominant frequencies appear, these vibrations are originated at the main and tail rotors', similarly to the X axis. Figure 11: Y axis fuselage vibrations for mbl 1 = kg, mbl 2 = kg, mbl 3 = kg and mbl 4 = kg and on the tail rotor they are; mbltl 1 = kg and mbltl 2 = kg. Figure 9: X axis fuselage vibrations for mbl 1 = kg, mbl 2 = kg, mbl 3 = kg and mbl 4 = kg and on the tail rotor they are; mbltl 1 = kg and mbltl 2 = kg. From the spectrogram of frequencies shown in Figure 10 (the window length is reduced in order to check the noise and other additional frequencies are not A comparison can be carried out for the vibrations presented in these sections. Clearly, the aerodynamic load is a source of vibrations on the helicopter's fuselage. The obtained spectrograms for hover flight agree with theoretical predictions: a) there is an important source of helicopter vibrations, the aerodynamics forces [7], b) the aerodynamic loads on a helicopter rotor blade vary considerably as it moves around the rotor disc. These loads arise from the aerodynamic forces on the rotor blades, together with

7 ISBN Comité Español de Automática de la IFAC (CEA-IFAC) 479 the inertial forces produced by the flap and lag motions of the blade [1]. early stage and the authors expect to develop further analogies with experimental results in future work. In summary, a full helicopter model has been modelled using VehicleSim. Spectrograms analysis on the fuselage s roll and pitch axes captured the appearing vibrations as a consequence of the aerodynamic load in hover flight, these results have been compared to dynamic vibrations obtained with identical helicopter model under the action of unbalance of masses on the rotors. As a result of this, the vibrations in hover have been shown to satisfy the predicted behaviour. References Figure 12: Fuselage vibrations Spectrogram on the Y axis for mbl 1 = kg, mbl 2 = kg, mbl 3 = kg and mbl 4 = kg and on the tail rotor they are; mbltl 1 = kg and mbltl 2 = kg. 7 CONCLUSIONS The helicopter model under study is on Sikorsky configuration, the model reproduces the dynamic behaviour of a helicopter, which is capable to transmit perturbations from the main rotor to the fuselage in form of vibrations. The model has been implemented in VehicleSim, a program allows to define the systems as composition of several bodies and ligatures by using a parental relationship parent/child structure. This work has presented a helicopter aerodynamic model in which the blade element theory has been used for implementation hover flight. This is important in order to study and analyze the vibrations appearing in the fuselage as a consequence of aerodynamic load under these flying conditions. Various tests under the action of these conditions were carried out in order to study pure vibrations appearing on the fuselage roll and pitch axes. In hover flight and under unbalance of masses on both rotors, fuselage vibrations spectrograms were obtained and analyzed by using a short time Fourier transform process, various cases were considered, when the aerodynamic load for hover flight was included in the dynamic helicopter model, the obtained results match those predicted by theoretical approaches. In addition to this, these vibrations were compared to dynamic vibrations generated with the same helicopter model in absence of the aerodynamic load. As a consequence, the spectrograms were also studied and these showed a reasonable discrepancy according to the expected behaviour introduced by the aerodynamic model. These results are still on an [1] Bramwell, A. R. S., Done, G., Balmford, D. (2001) Bramwell's Helicopter Dynamics. Butterworth-Heinemann. [2] Castillo-Rivera, S. (2014) Advanced Modelling of Helicopter Nonlinear Dynamics and Aerodynamics. PhD Thesis. School of Engineering and Mathematical Sciences. City University London. [3] Castillo-Rivera, S., Tomas-Rodriguez, M., Marichal-Plasencia, G., N. (2014) Helicopter Main Rotor Vibration Analysis with Varying Rotating Speed. XXXV Jornadas de Automatica. pp ISBN-13: [4] Castillo-Rivera, S., Tomas-Rodriguez, M., Marichal, G.,N., López, A. (2013) Estudio de la interacción del fuselaje y el movimiento de aleteo de las palas del rotor principal en un helicóptero. XXXIV Jornadas de Automatica. pp ISBN [5] Ferrer, R., Krysinski, T., Aubourg, P., Bellizi, S. (2001). New Methods for Rotor Tracking and Balance Tuning and Defect Detection Applied to Eurocopter Products American Helicopter Society 57th Annual Forum, Washington, DC, May [6] vehiclesim/index.php. [7] Johnson, W. (1980) Helicopter Theory. Princeton, NJ: Princeton Univ. Press. [8] Keysan, O., Ertan, H. Higher Order Rotor Slot Harmonics for Rotor Speed & Position Estimation. 12th International Conference on Optimization of Electrical and Electronic Equipment, OPTIM [9] Leishman, J. G. (2007) Principles of Helicopter Aerodynamics. Cambridge University Press.

8 ISBN Comité Español de Automática de la IFAC (CEA-IFAC) 480 [10] Marichal, G.,N., Tomas-Rodriguez, M., Lopez, A., Castillo-Rivera, S., Campoy, P. (2012) Vibration Reduction for Vision System on Board UAV using a neuro-fuzzy Controller. Journal of Vibration and Control. DOI / [11] Nguyen K. (1994) High Harmonic Control Analysis for Vibration Reduction of Helicopter Rotor Systems. NASA Technical Memorandum [12] Seddon, J. (1990) Basic Helicopter Aerodynamics. Blackwell Scientific Publications (BSP) Professional Books. [13] Sharp, R, S., Evangelou, S., Limebeer, D, J, N. (2005) Multibody aspects of motorcycle modeling with special reference to Autosim, Advances in Computational Multibody Systems, J. G. Ambrosio (Ed.), Springer-Verlag, Dordrecht, The Netherlands, [14] Tomas-Rodriguez M., Sharp R. (2007) Automated Modeling of Rotorcraft Dynamics with Special Reference to Autosim. Automation Science and Engineering. CASE IEEE International Conference, pp: [15] Watkinson. J. (2004) The art of the helicopter. Elsevier Butterworth-Heinemann.