Browse Topic: Finite element analysis
Emerging technologies in the field of electrified propulsion systems offer a promising solution to reduce the dependence on fossil fuels and improve efficiency. However, the design of high-power density electric machines introduces new challenges, including limited passive cooling potential and the issue of the weight of electric motors. To address these challenges, this paper considers analysis and design methods for high torque-to-weight ratio axial flux motors. A magnetic equivalent circuit model coupled with a lumped parameter thermal network is developed for design space exploration and optimization. This inexpensive analytical model predicts the performance of a single-stator dual-rotor axial flux motor based on geometry, loading condition, and slot and pole pair combination. To enable comparisons against real-world data, the optimization study was demonstrated using the hover mission requirements from the Research Aircraft for eVTOL Enabling techNologies (RAVEN) vehicle to minimize the mass of the motor. In tandem with the analytical model, a higher-fidelity finite element model was also developed, and good agreement between predicted power and efficiency was demonstrated across a range of axial flux motor designs. The lightest weight design that satisfied the hover mission requirements was the 12 pole pair 27 slot (12PP 27S) configuration with a fixed weight of 9.28 kg. The analytic model undersized the output power of the electric motor by approximately 9% across a range of slot and pole pair combinations.
NASA's successful demonstration of powered flight on Mars through the Ingenuity Helicopter, as part of the Mars 2020 Perseverance rover mission, has led to the development of next generation Martian rotorcraft. The future of Martian rotorcraft has evolved to include high payload-carrying vehicles to possibly contribute to planetary science missions, which will require improved flight dynamics and rotor aerodynamic performance to fly at nominally high forward flight speeds and at higher flight altitudes. To ensure the feasibility and viability of successful mission performance, it is also critical to mature the structural design for advanced Martian rotorcraft to bridge the gap between the best practices of the spacecraft and aircraft communities. This paper focuses on the structural analysis of a Mars Science Helicopter (MSH) blade using finite element methods. Multiple loading conditions including launch and operational flight were applied to investigate the blade’s structural integrity. The blade’s modal natural frequencies were also analyzed to investigate the blade's dynamic behavior.
The paper describes a method for optimal design of a helicopter tail shaft that considers rotordynamic effects from long shaft assembly. The tail shaft transmits power from the main gearbox (MGB) to the tail rotor of the helicopter and operates at high speeds that may exceed 6000 rpm. While higher speeds allow for weight reduction, they also pose risks associated with supercritical operation, necessitating careful design optimization. The objective of the optimization is to maximize the first three transverse natural frequencies with the constraint of the safety parameter (avoidance of the resonance/critical zone) while minimizing the weight of the system. A Non-Dominated Sorting Genetic Algorithm (NSGA-II) is used to obtain the solution to this multiobjective optimization problem, which involves shaft design variables such as length, outer diameter, and wall thickness. In addition, the optimization framework also incorporates system related design variables, including the stiffness of tail shaft bearing supports, the location of bearings, and coupling characteristics, to comprehensively evaluate and enhance the system performance. A rotordynamics model utilizing Timoshenko beam finite elements is deployed to predict natural frequencies.
Electric vertical take-off and landing vehicles are proposed as a viable solution for urban air mobility due to their potential for reducing carbon emissions, noise, and operational costs. However, the shift towards electrified aircraft introduces new thermal management issues due to the excess heat generated by electric motors and power electronics. This heat is challenging to dissipate during the mission, resulting in transient motor temperatures, especially during high-power mission segments. In addition, electrified aircraft also encounter design challenges associated with the fixed weight of electric motors and batteries. To address these challenges, this work presents a multifidelity framework for performing shape optimization of an electric motor subject to performance, geometric, and thermal transient constraints. A preliminary sizing of the electric motor is performed using a low fidelity Fourier series model. Next, the sizing is refined by utilizing a coupled electromagnetic-thermal finite element model of the the motor physics. To demonstrate the framework, a numerical optimization is performed for a hover hold mission with a relevant scale eVTOL vehicle, reducing the structural mass of the motor by 2.7kg while ensuring power and thermal constraints are satisfied.
Finite element analysis of gearbox and transmission assemblies is usually a process that takes several weeks of meshing and geometry cleanup, running the simulation, checking the results, fixing the inevitable mistakes, then rerunning and checking again. This process doesn’t even account for the addition of design changes which make the whole process start over. This paper is meant to explore some of the new meshless simulation tools and see how they can be leveraged to more quickly produce results, and allow for better design changes that are driven by the simulation needs. We will show how leveraging meshless analysis leads to better designs for complex assemblies and parts.
Carbon/epoxy stiffened panels are being increasingly used in transport rotorcraft. The reduced mass density and high stiffness of carbon/epoxy composites can lead to higher levels of vibration relative to comparable metallic structures, which themselves can have vibrations and interior noise high enough to damage the hearing of crew and passengers. The current investigation explores a method to reduce the vibration of carbon/epoxy stiffened panels by introducing thickness tapers known as acoustic black holes (ABHs). The ABH feature is integrated into either the stiffeners or plate of a representative stiffened panel configuration. A finite element (FE) parametric study was used to guide designs that reduce the vibration of the panel without compromising the compressive buckling capability or mass of the panel. FE studies showed that a 30 ply to 12 ply thickness taper longitudinally oriented in the blade stiffener can reduce vibrations and increase compressive buckling capability. Carbon/epoxy panels were manufactured using a low-cost out-of-autoclave material with simple molding. Experimental testing concluded that integrating the ABH into the stiffeners longitudinally helped to reduce the broadband vibration by 5 dB and increase the buckling load (+4.3%) and collapse load (+16.5%) without increasing the mass greatly compared to a traditional baseline design.
Accurate simulation of fluid-structure interactions (FSI) is critical for designing aircraft systems, particularly for applications involving fuel tank sloshing and large deformations. Traditional added mass methods often fail to capture the nonlinear and frequency-dependent behavior of these coupled systems. This study applies the Finite Pointset Method (FPM), a mesh-free computational fluid dynamics (CFD) technique, coupled with an explicit finite element solver, to predict complex FSI phenomena. Validation is performed using benchmark experiments, including a harmonic tank sloshing test and a guided plate ditching scenario, with results demonstrating strong agreement with measured pressures and structural responses. Additional validation on a composite fuel tank drop impact test confirms FPM's ability to model large deformations and rupture under dynamic loading. The findings highlight FPM's robustness and adaptability for aerospace FSI problems, offering a powerful alternative for virtual prototyping and certification workflows where conventional methods are insufficient.
This study investigates the stress concentration and damage tolerance of lug structures, with an application example using the horizontal tail plane lug of a light utility helicopter. Using Finite Element Analysis (FEA), stress distributions around the lug hole were simulated under varying load conditions to understand how different loading angles and magnitudes affect stress concentrations. A machine learning approach was employed to predict stress distributions based on a dataset generated from FEA simulations. Several regression models were tested and Random Forest Regression model yields the best predictive accuracy among the others. The study also incorporates a flaw tolerance analysis using the NASGRO® software to calculate the crack growth characteristics of the horizontal tail plane lug structure under service loading. The results highlight the importance of stress distribution variability and identifying the most critical point of the lug structure under service loading with changing angle and amplitude. This research provides insights into the structural integrity of lug components under dynamic loading, contributing to more reliable flaw tolerance assessments for aerospace applications using machine learning techniques.
Helicopter rotor blades with several different parts, multiple load paths and/or springs and dampers can be modeled as a multibody system, into which finite element descriptions of flexible bodies can be integrated. When doing so, model order reductions can be necessary for robustness and/or performance reasons. A known drawback of such reductions is that the isolated modes of the particular bodies may not adequately describe their actual deformations in the multibody system. To alleviate this problem, the paper proposes a Craig-Bampton reduction for the flexible bodies. Compared to a standard modal reduction, the additional consideration of static interface modes in the Craig-Bampton approach significantly improves the prediction of eigenfrequencies and mode shapes, as demonstrated for a segmented steel beam with a single load path. Using the same approach, a bearingless rotor blade with multiple load paths is modeled by two beam segments. The model is assessed by code-to-code comparison with a CAMRAD II reference model. The consideration of the tension interface degree of freedom of the inner segment (flexbeam) allows for the accurate prediction of eigenfrequencies at varying rotor speeds, including the effect of centrifugal stiffening – which is not appropriately covered with a standard modal reduction. With the Craig-Bampton method, the mode shapes are plausible and in overall good agreement with the reference model. Despite these benefits, deficiencies are identified that still need to be improved. Discrepancies in the blade’s torsion eigenfrequency prediction are observed, as well as anomalies in the mode shapes that are potentially related to the flexbeam, that is – despite the consideration of interface modes – too kinematically restricted.
A typical helicopter drive system consists of a multi-stage gearbox with highly loaded dynamic components such as gears, shafts, and bearings, crucial for safe flight and landing. Planetary reduction stages are commonly used in the final reduction stage of rotorcraft main gearboxes due to their ability to handle high torques at high gear ratios within a compact envelope. The planet gear, a critical component in this arrangement, is subjected to significant loads on both flanks of its teeth and must meet stringent weight and assembly requirements, leading to a thin rim design with integrated bearing races. This design makes the planet gear susceptible to relevant reduction of its fatigue life. This paper explores analysis methods to evaluate the damage resistance of the planetary stage assembly, focusing on the planet gear. The study aims to assess the "growth" or "no growth" condition of the planet gear against defined flaw defects. An iterative calculation loop determines the critical length and position of a crack that may lead to full crack propagation and, in worst cases, to system jamming. Initial crack propagation simulations use NASGRO software, with stress fields derived from a non-linear FEM of the planet gear availing of detailed Transmission3D model for teeth meshing forces evaluation. Further additional analysis can involve a dedicated FE model of the crack, iteratively updating its geometry. The impact of crack propagation on the remaining components of the planetary stage assembly is also addressed, considering the unbalanced load conditions caused by stiffness loss in the planet gear. The dissertation object of this paper aims to outline a comprehensive, effective and efficient procedure to determine the maximum allowable defect size for "no growth" condition and the operational hours until failure, providing a robust approach to support the strength substantiation of the involved components.
Composite materials have long been used in rotorcraft structural applications due to their high strength-to-weight ratio. However, they can also be prone to unique types of defects such as resin pooling, porosity, and delamination which can impact their structural performance. Resin pooling can occur when excess resin accumulates in certain areas of the composite laminate. This paper presents a method of finite element analysis to quantify the effect of the resin lens on the structural strength of a specific laminate. This method was used to successfully validate the structural integrity of several composite torque tubes with resin-rich indications, which were initially rejected at inspection.
Rotorcraft experience significant vibrations due to periodic aerodynamic forces and moments on the rotor blades and wings. Rotor torque damping is a novel vibration damping method which uses small torque perturbations from the main electric motor to reduce vibrations. The large inertial and aerodynamic rotor loading and relatively high frequency torque perturbations mean that the rotor speed changes are small, so the rotor thrust and flight control performance are not significantly affected. This paper investigates the application of electric motor torque control for damping structural vibrations of an aircraft. The structural dynamics of the aircraft are represented using a finite element model of a quad tiltrotor eVTOL. Using collocated angular rate feedback on all four rotors provides more than 10% damping in controllable modes. The RMS value of flap-wise angular rate can be reduced by 91% with less than 1.2 RPM rotor speed change in response to a 20% vertical step gust in airplane mode. For N/rev disturbance cancellation, an optimal controller is designed assuming known disturbance location and frequency for active vibration control (AVC). The transfer matrix of a single cantilevered wing is calculated and used to feed forward harmonic rotor torques. The wing undergoes aerodynamic disruptions at N/rev and the harmonic controller reduces N/rev shear force and bending moment at the root by 20% and 58% with less than 1 RPM rotor speed change, respectively.
Shot peened components present a challenge for the structural analyst when nicks, scratches and gouges are discovered. A common repair scheme calls for blending away of the defect with an appropriate grit abrasive. Though the blending operation removes the defect, it also takes away a portion the beneficial compressive layer as well as the cold-worked material. Large repair facilities may have touch-up shot peen capability but technicians in a field repair setting typically do not. If the shot peen cannot be restored, the structural analyst must have a method to quantify the effect on fatigue life of the repaired part. The purpose of this technical paper is to substantiate analytical techniques for evaluating the fatigue life of a shot peened part after a blend operation. In addition to practical methods to estimate the magnitude of the residual stresses, a numerical method is introduced using finite element modeling of shot peen impacts with non-linear finite element code and validation by a simulated Almen strip.
This work proposes an experimental and numerical activity aimed at developing methods to evaluate the strength and toughness of Kevlar/Epoxy composite fastened joints used in aeronautical structures and exposed to high energy impacts. Experiments were conducted using an Arcan rig that allowed applying various loading conditions, ranging from pull-through to bearing. A non-linear model of the material based on a bi-phasic decomposition and hybrid meshing technique was built and calibrated. The material model was used to develop a high-fidelity model of the junction to simulate the pull-through test with the Abaqus/Explicit finite element solver. The results of the analysis point out that the implemented progressive damage laws are capable of achieving an appreciable experimental-numerical correlation, both from the qualitative and the quantitative standpoint. Therefore, the combined experimental-numerical approach is promising for developing a validated numerical tool capable of predicting the overall response of different junctions with minimal experimental effort, so to provide data for simulating impact scenarios at the rotorcraft structural scale and designing critical joints.
An accurate critical speed prediction of shafting systems in rotorcraft is required during preliminary design, so that dynamic loads do not lead to premature component failure within the full operational speed range, i.e. from stationary to maximum operational speed. If all modes are above the operational speed range, the shafting systems is considered subcritical and when design constraints do not allow for this type of design and so one or more critical speeds must be passed through before the shaft reaches its maximum speed the shafting system is considered supercritical and deflection limiters are required. Analytical simulations of the critical speeds of a shafting system can not only assist designers in making decisions in the earlier phase of design, but also helps mitigate risk during the qualification testing, ground run and flight test of the aircraft. Moreover, there are three factors important for an accurate critical speed prediction, i.e. gyroscopic effect, centrifugal force (CF) stiffening effect, or stress stiffening effect, and boundary conditions. The current paper focuses on the first two factors, especially the stress stiffening effect, but the discussion of the boundary conditions will be in a follow up paper. Ultimately, with the advancements of finite element analysis software, and the parallel processing provided by High Performance Computing, high fidelity finite element modeling of rotorcraft shafting system to assess critical speed is possible and practical.
This paper introduces a Multidisciplinary Design and Optimization (MDO) approach for the design of a tiltrotor wing, utilizing as test case a semi-wing with integrated nacelle and rotor. Structural integrity is assessed via stress analysis on a GFEM, which also forms the basis for a coupled wing-rotor aeroelastic model to ensure whirlflutter stability. Aerodynamic performance is assessed through CFD analysis of two-dimensional wing's airfoil shape. The MDO workflow leverages three levels of design space control that can influence the structural response of the wing: other than controlling the structural properties of composite materials, the internal wing-box architecture and external airfoil shape are modified acting directly on the FEM by means of a mesh morphing technique. This methodology allows for the use of mid-fidelity finite element models, bypassing CAD reshaping and remeshing. Validation tests confirm the approach's effectiveness in producing optimized designs. Additionally, the study explores surrogate models as efficient alternatives to CFD simulations, yielding sufficiently accurate results while reducing computational costs and the MDO simulation time.
Electric Vertical Takeoff Landing (eVTOL) aircraft feature heavy electric motors, battery packs, and rigid fixed-pitch rotors supported on flexible arms. Under substantial time-varying aerodynamic loads associated with variable rotor speeds and, with low intrinsic damping, such lightweight arms respond in bending and torsion at relatively high levels. In this paper, two methods of reducing vibration response in the operating frequency range are explored, one based on damping, the other on stiffness. A tailored particle impact damper system was evaluated experimentally to address near-periodic vibration over a range of frequencies. A forced torsional response test showed consistent 50% vibration reduction, with a 5% mass penalty. To stiffen the system, a cross-braced strut approach linked two arms such that the natural frequencies of their torsion modes would be increased beyond the rotor operating frequency range. A finite element model was developed and validated for a representative eVTOL configuration. Validation was conducted using a scale model aluminum beam set. The addition of a cross-braced strut efficiently stiffened the system, increasing its natural frequency by almost 120%, thus greatly reducing resonant torsional vibration within the operating range. Both approaches to vibration reduction for variable-speed eVTOL aircraft merit continued consideration and research.
A state-of-the-art emerging progressive damage failure analysis tool CDMat has been successfully applied to multiple material systems on open-hole tension and compression, and double shear bearing laminate coupons under static and fatigue loading including simulation to ultimate failure. CDMat also successfully demonstrated component-level strength/fatigue analysis under the Air Force Composite Airframe Life Extension (CALE) and the Fail-Safe Technologies for Bonded and Unitized Composite Structures (FASTBUCs) Programs. Building on the success of CDMat an integrated software solution for certification and sustainment of rotorcraft primary composite structures is being developed. A method and an algorithm for fatigue crack growth simulation in laminated structures are proposed to improve the accuracy of CDMat fatigue predictions. The method is based on using cohesive material model, tracking material points at the crack front, and calculating the pointwise energy release rate employing the J-integral. The algorithm was implemented as a set of user material subroutines developed within the framework of explicit finite element formulation for ABAQUS. The effectiveness of the method is demonstrated on several examples of Mode I and II fatigue crack growth.
This paper presents an open-loop hover experiment and analysis for a 4-blade Mach-scaled Seoul National University Flap (SNUF) rotor. A detailed finite element analysis is attempted to predict allowable experiment range that provides sufficient structural integrity. Multi-body dynamic analysis DYMORE and cross-sectional design program VABS are used to analyze the present trailing-edge flap rotor blade, and the flap hinge stiffness is calibrated on the static bench test. Ground testing on the present rotor shows a linear strain-displacement response, and the relevant result shows better than 80% correlation against DYMORE prediction. Appropriate test matrices are constructed and two of those are attempted herein. The first one is the baseline no-actuation collective sweep test at two different rotating speeds at tip Mach of 0.22 and 0.3, respectively. The results are utilized to correlate between the momentum theory and free wake empirical parameters. Next, a single active flap blade test is attempted to assess the trailing-edge flap driving component. It is found that the dynamic trailing-edge flap deflection result needs to be both electrically and mechanically isolated from the test stand. In the future, trailing-edge flap deflection will be recorded for 1 - 5/rev activation at tip Mach 0.5, while four-blade actuation engaged. The frequency response of the trailing-edge flap mechanism will be identified, and 1/rev tracking control will be attempted.
This study explores the best vibration reduction using a multicyclic controller through an individual blade control (IBC) actuation scheme for a lift-offset coaxial helicopter in high-speed flight. The rotorcraft dynamics model consists of coaxial, three-bladed counter-rotating rotors and a finite element fuselage stick model constructed based on the measured data of the XH-59A helicopter. The two-way coupled rotor-body vibration analysis results exhibit excellent correlations with the test data for rotor hub loads and airframe vibrations. The best actuation scenarios are sought for the minimum vibration of the vehicle using either open- or closed-loop control scheme. It is shown that the IBC actuation effectively reduces the vibrations at both locations of the rotorcraft. The co-reduction of 3P (per rotor revolution) and 6P vibration of the rotorcraft is achieved using the multicyclic control with offline system identification. A multicyclic harmonic IBC actuation enables to suppress the rotorcraft vibration by 81.4% and 3P pilot seat vibration by 92%, respectively, as compared to the uncontrolled case, leading to a significantly reduced vibration level (below 0.05g) of the rotorcraft. The closed-loop multicyclic control using the identified system and the aircraft model shows a good correlation ensuring the suitability of the present optimal control simulations.
Carbon fiber reinforced epoxy composite stiffened panels are increasingly being used for structural components in large transport rotorcraft. However, problems are arising with high levels of vibration and interior noise due to the increased stiffness-to-density ratio of composites. The current investigation explores the potential of reducing vibrations in carbon/epoxy stiffened panels with the integration of acoustic black holes (ABH), namely features that incorporate a power law thickness taper. The proposed approach involves designing a taper into the thickness of the blade stiffeners as well as the thin plate. Integration of ABHs into the fuselage structure has the potential to reduce broadband vibrations. Multiple parametric studies with either an ABH integrated into the blade stiffener or a grid of ABHs integrated into the plate were conducted, and the tradeoffs between vibration amplitudes, panel mass, and compressive buckling load were examined. Carbon/epoxy panels were fabricated using vacuum-bag-oven processing with out-of-autoclave prepreg and verified to be of good quality. The integrated velocity response, a proxy for the radiated noise from a panel, and compressive buckling were simulated using finite elements. Comparisons were made to experimentally measured data from modal testing and compression buckling testing. Experimental results indicated that when an ABH is integrated into the blade stiffener and 15 ABHs are integrated into the plate in a grid configuration, the panel mass was unchanged, the integrated velocity response decreased by 2.82 dB, and the buckling load increased by 2.9% compared to a baseline non-tapered design.
This paper details an analysis methodology for a primary structure component on a tandem rotor helicopter that has been shown to experience fatigue damage in operation. The primary structure component is a web in the aft pylon of the helicopter. The web carries a complex set of loads in flight with various forces and moments applied along its boundaries and rotor torque reacted around a large rectangular cutout in the web. Due to the complex loading applied to the web, there is no clear location that can be considered to carry a "gross" stress, rendering traditional hand calculation methods (such as the use of stress concentration factors applied to a gross stress) impractical. The analysis detailed in this paper considers the application of flight loads to Finite Element Models to determine stresses in the web, which are used to evaluate fatigue life based on various flight conditions.
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A mesh partitioner was developed for large-scale 3D rotor structural dynamic models containing higher-order 3D finite elements and multibody joints. A parallel iterative substructuring solver was built to operate on the partitioned data structures. The algorithmic scalability of the solver was demonstrated on three sample problems of progressively increasing complexity; an elementary uniform beam, a real rotor blade - the NASA TRAM (1/4 scale V-22 model blade), and the full TRAM blade and hub assembly containing four flexible parts connected using six joints. The key conclusion is that a multibody blade and hub assembly can be partitioned and solved in a parallel and scalable manner. Rotor structures of up to 6.6 million degrees of freedom are solved on up to 2048 processors with detailed studies of scalability and efficiency. The uniform cantilevered beam is able to achieve a speedup of 1000 times, while the realistic rotor is able to achieve a speedup of over an order of magnitude, reducing the computational time to a matter of seconds. The use of the specialized mesh partitioner, with a robust corner node selection strategy, is key to minimizing computational time.
eVTOL sizing is tackled with a Multi-Disciplinary Optimization problem with nonlinear constraints in this work, focusing on UAVs with distributed vertical lift. Several optimization schemes are investigated for including airframe sizing with finite element analysis, vehicle trim, and blade aerodynamic shape design. The iterative weight convergence loop is replaced by a slack variable and equality constraint for the sizing optimizer. Airframe sizing and weight minimization (with stress inequality constraints) may be driven either by the sizing optimizer, or by a separate optimizer within the various constraint functions in a nested structure. It is preferable to drive the trim variables using the sizing optimizer; if a particular design cannot be trimmed, this information is propagated to the sizing optimizer through the corresponding equality constraints. The all-at once optimization strategy yields results in the shortest time compared to the other methods. Using modified momentum theory for rotor performance, all gradient-based optimizations from different starting points converged to the same minimum, indicating that the design space is convex for the chosen bounds and objective function. Blade shape design with BEMT is also included in the sizing, either directly with blade twist and taper as additional design variables, or indirectly through a response surface. The methodology is demonstrated on the sizing of two package delivery vehicle configurations (a quadrotor and a lift-augment quadrotor biplane tailsitter) for a mission with 10 km radius of action. The cruise airspeeds for the two configurations are also identified as part of the sizing/optimization. The quadrotor is more suited for this point mission owing to its lower empty weight compared to the quad-biplane, which has better cruise efficiency but higher empty weight.
The present paper designs and validates a finite element bird model in order to develop a useful tool for the numerical simulation of an aeronautical bird strike event. The bird is simulated in Abaqus/Explicit environment using the Smoothed-Particle Hydrodynamics (SPH) technique. This formulation is a common approach to the problem, as noticed in many published works that investigate the bird strike problem using other solvers such as LS-Dyna. They are taken as a starting point of the present work in the definition of the bird model initial geometry and equation of state. A comparison and a correlation between some experimental tests and their simulations was conduct, in order to develop and validate the bird numerical model. In particular, impacts against rigid targets, such as plates and wedges, and against deformable ones are evaluated. The result is a validated SPH FE bird model, which can be involved in the next bird strike analysis being a reliable numerical tool.
This work develops tailboom aerodynamic loading for a TH-1H helicopter in hover by integrating a finite element model (FEM) and in-service strain time histories in accordance with structural mechanics and aerodynamics principles. The FEM is a whole aircraft model used to establish stress spectra at critical aircraft components for fatigue and fracture analyses from main rotor and tail rotor forces. The in-service time histories are the responses from sixteen uniaxial strain gages attached to the tailboom primary longerons and the corresponding structure inside the main cabin. Five separate loading modalities are used as FEM static load cases. Published experimental drag coefficients are used to develop two aerodynamic pressure load distributions for the tailboom as well as separate left and right elevator pressure loads. The fifth case is a lateral tail rotor force. Weighting factors are determined for these five modalities so that the weighted sums of the FEM strains best-fits the measured strains at the sixteen gage locations. This fitting process is executed for each time step of each strain gage in a given hover regime, as well as for the average gage values for the duration of the regime. Weighting factors are evaluated for admissibility (i.e. non-negative values, bounded magnitudes that do not produce unrealistically high stresses). The results are compared against the measured strains. The mechanics of the tailboom structure is also evaluated with respect to strains, longeron loads, and netsection bending moments. The findings highlight that the longerons (where the strain is measured) account for approximately two-thirds of the tail boom bending moments; the external skins and stiffeners provide the balance of the moments. Two load modality combinations emerged as best-fits: tail boom aerodynamic pressure loading plus tail rotor force, and elevator pressure loading plus tail rotor force. Both show varying levels of fidelity to the measured data, which suggests that additional load modalities should be considered, and that additional instrumentation of the skins should be implemented for future strain surveys.
This paper describes an experimental-numerical technique for evaluating the full 6 × 6 stiffness matrices for beams based on measured strains using digital image correlation (DIC). The general formulation makes the method well suited for isotropic beams with simple cross-sectional configurations or beams made of anisotropic materials with complex geometries, as typically exhibited in composite rotor blades. A 2-D finite element code, SectionBuilder, is used to generate a finite element mesh of the cross-section and evaluate the warping field, which is then combined with the experimental strain data to calculate the stiffness matrix. A detailed error analysis is performed to allow for the propagation of the experimental errors into the stiffness calculation and provide an uncertainty quantification for use in comprehensive analysis codes. Experimental results are presented for an isotropic beam and two composite rotor blades. Overall, the stiffness properties from the experimental measurements and numerical models showed good agreement and the experimental measurements were able to capture all the expected non-zero stiffness components.
Robust and accurate predictions of rotorcraft aerodynamic and structural loads and vibrations are essential for designing advanced rotorcraft. The aerodynamic environment around the rotors is nonlinear and unsteady, the rotor and its wake interact strongly with fuselage and empennage to drive the structural vibrations. All of the components are elastic structures linked with one another by structural and aerodynamic interactions requiring a high fidelity coupled analysis. This paper presents simulations and validations for two examples: the aerodynamic interactions of a powered rotor - fuselage - empennage wind tunnel model using CFD (Computational Fluid Dynamics), and the structural loads and vibrations of a flight test aircraft using coupled CFD/CSD (Computational Structural Dynamics) - FEA (Finite Element Analysis). The NASTRAN FEA generated an elastic fuselage modal model which was coupled to the CFD/CSD tools in the CREATETM-AV HELIOS framework. The interactional aerodynamics simulation focused on lower advance ratio cases, which have a particularly strong rotor wake - empennage interaction and compared time averaged and periodic aerodynamic loads and flow velocity fields to experiment. Trends matched well, but quantitative differences remained, particularly at the lowest advance ratios. The full aircraft simulations were performed at increasing degrees of complexity and coupling. The agreement with measured rotor blade structural loads and horizontal stabilizer vibrations was best using the most complete model of the main rotor, tail rotor, fuselage and empennage.
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