Ngo Anh Vu,Ja Woo L,Tuan Phuong Nam L,Song Thanh Thao Nguyn

aDivision of Computational Mechatronics,Institute for Computational Science,Ton Duc Thang University,Ho Chi Minh City 756636,Vietnam

bFaculty of Electricalamp;Electronics Engineering,Ton Duc Thang University,Ho Chi Minh City 756636,Vietnam

cDepartment of Aerospace Information Engineering,Konkuk University,Seoul 143-701,Republic of Korea

dFaculty of Mechanical Engineering,Industrial University of Ho Chi Minh City,Ho Chi Minh City 727905,Vietnam

eDepartment of Aerospace Engineering,Ho Chi Minh City University of Technology,Vietnam National University-Ho Chi Minh City,Ho Chi Minh City 740015,Vietnam

A fully automated framework for helicopter rotor blades design and analysis including aerodynamics,structure,and manufacturing

Ngoc Anh Vua,b,*,Jae Woo Leec,Tuan Phuong Nam Led,Song Thanh Thao Nguyene

aDivision of Computational Mechatronics,Institute for Computational Science,Ton Duc Thang University,Ho Chi Minh City 756636,Vietnam

bFaculty of Electricalamp;Electronics Engineering,Ton Duc Thang University,Ho Chi Minh City 756636,Vietnam

cDepartment of Aerospace Information Engineering,Konkuk University,Seoul 143-701,Republic of Korea

dFaculty of Mechanical Engineering,Industrial University of Ho Chi Minh City,Ho Chi Minh City 727905,Vietnam

eDepartment of Aerospace Engineering,Ho Chi Minh City University of Technology,Vietnam National University-Ho Chi Minh City,Ho Chi Minh City 740015,Vietnam

This study describes an integrated framework in which basic aerospace engineering aspects(performance,aerodynamics,and structure)and practical aspects(configuration visualization and manufacturing)are coupled and considered in one fully automated design optimization of rotor blades.A number of codes are developed to robustly perform estimation of helicopter configuration from sizing,performance analysis,trim analysis,to rotor blades configuration representation.These codes are then integrated with a two-dimensional airfoil analysis tool to fully design rotor blades configuration including rotor planform and airfoil shape for optimal aerodynamics in both hover and forward flights.A modular structure design methodology is developed for realistic composite rotor blades with a sophisticated cross-sectional geometry.A D-spar cross-sectional structure is chosen as a baseline.The framework is able to analyze all realistic inner configurations including thicknesses of D-spar,skin,web,number and ply angles of layers of each composite part,and materials.A number of codes and commercial software(ANSYS,Gridgen,VABS,PreVABS,etc.)are implemented to automate the structural analysis from aerodynamic data processing to sectional properties and stress analysis.An integrated model for manufacturing cost estimation of composite rotor blades developed at the Aerodynamic Analysis and Design Laboratory(AADL),Aerospace Information Engineering Department,Konkuk University is integrated into the framework to provide a rapid and dynamic feedback to configuration design.The integration of three modules has constructed a framework where the size of a helicopter,aerodynamic performance analysis,structure analysis,and manufacturing cost estimation could be quickly investigated.All aspects of a rotor blade including planform,airfoil shape,and inner structure are considered in a multidisciplinary design optimization without an exception of critical configuration.

1.Introduction

Rotor blade designs have been the main research in the rotorcraft industry for the past decades.Challenges still exist due to difficulties in dealing with integrated disciplines.Studies have been used to solve isolated problems of aerodynamics,structure,dynamics,performance,noise,etc.Recently,a number of researchers have focused on high-fidelity approaches for rotor blade design and analysis.Pape and Beaunier1created an aerodynamic optimization for helicopter rotor blade shape in hover based on the coupling of an optimizer with a three-dimensional Navier-Stokes solver.Morris and Allen2developed a generic aerodynamic optimization tool based on computational fluid dynamics(CFD)for helicopter rotor blades in hover.Imiela3created an optimization framework for helicopter rotors based on high-fidelity coupled computational fluid dynamics/computational solid mechanics analysis.The optimization framework was first applied to various optimization problems in hover starting with an easy task of optimizing the twist rate for a 7A model rotor.The last optimization in hover involved all design parameters,namely twist,chord,sweep,anhedral,transition points of two different airfoils,and starting point of the blade tip showing its superiority over simpler optimization problems with respect to the achieved improvement.3

Chattopadhyay et al.4,5performed an integrated aerodynamic/dynamic optimization to reduce the blade weight and 4 per revolution vertical shear in forward flight.Design variables are flap and lag stiffness,taper ratio,and root chord at seven spanwise stations.Walsh et al.6,7performed a study for integrated aerodynamic/dynamic/structural optimization of helicopter rotor blades.This study minimized a linear combination of required power(in hover,forward flight,and maneuver)and vibratory hub shear.The design variables included rotor blades planform,blade stiffness,and turning mass locations.

In the early 1990s,several aeroelastic analyses of composite helicopter rotors were performed.A good background on optimization ofcompositestructureswasgiven by Jung8,Volovoi9,and Gurdal10et al.Ganguli and Chopra11studied aeroelastic optimization of a helicopter rotor blade to reduce vibration and dynamic stresses.The studies were carried out for a four-bladed hingeless rotor consisting of a two-cell composite box-beam spar.The design variables were the ply angles of the box-beam walls.The first study of Ganguli and Chopra used a single-cell box beam model.However,realistic rotor blades were built as a multi-cell airfoil section.Therefore,they used a composite beam cross-sectional model based on the Vlasov theory,along with a comprehensive rotor aeroelastic analysis to optimize composite rotors.12–15Paik et al.16investigated a new approach for realistic rotor blade crosssectional optimization.The design variables used in this study were layer angles,layer thickness,and spar location.The objective function was the distance between the shear center(SC)and the quarter chord.Li et al.17extended this work by choosing a combination of the distances between the SC and the aerodynamic center(AC),the mass center(MC),and the aerodynamic center as the objective function.In reality,the layer thickness is usually a standard value which is not continuously changed.The number of layers is a realistic design variableforstructuraldesign.However,thischoicecould significantly change a structural configuration that solvers may not analyze during the design process.This study developed a process to combine these realities with current design optimization.Sensitive analysis specified smooth working of the framework.

Both outer and inner shapes of rotor blades affect the positions of shear and mass centers which specify dynamic characteristics of rotor blades.Asymmetric airfoils desired for better aerodynamics could weaken the structure and dynamic performance of rotor blades.Coupling analysis of aerodynamics and dynamics of rotor blades are topics of many researches.These studies require a lot of computer resources and are time-consuming.Therefore,an integrated framework quickly investigating all aspects of rotor blade configuration for multidisciplinary studies is a demand for designers.

Moreover,the practical aspect,manufacturing,has not been considered properly in the past because an integrated framework of theoretical aspects and manufacturing has not been built.A design for aerodynamics and dynamics may result in configurations of a rotor blade which is infeasible for manufacturing.Integrated models for manufacturing cost estimation and system performance evaluation of aerospace composite parts are implemented to provide a rapid and dynamic feedback for a designer or a product development team who performs manufacturing cost estimation and system performance evaluation to manufacture a new or existing product during early design processes.Many sub-modules are implemented in a manufacturing module.Those include the time estimation module for manufacturing processes,activity-based costing module,decision support system module,and manufacturing system performance evaluation module.Knowledge base data collected and computer-aided automated procedures are also provided in this implementation.18,19

This paper describes an integrated framework developed for aerodynamics,structure,and manufacturing analysis for realistic composite helicopter rotor blades.Each module is developed separately,and then integrated together to fulfill a fully automated process from helicopter aerodynamic performance analysis to manufacturing cost estimation and system performance evaluation.Thereby,all aspects including outer,inner configuration(airfoil shape,blade planform,thickness of each layer,position of each component,etc.)and manufacturing cost can be considered at the same time for the best rotor blades.The whole framework is integrated in the ModelCenter software.Robustness of the framework is achieved.The rotor blade configuration arbitrarily varies and is governed by realistic design variables without limited choices.Optimization results show that the integrated framework is necessary to trade-off among aerodynamic shape,structural characteristics,and manufacturing cost.

2.Integrated framework

The integrated framework is wrapped in ModelCenter as shown in Fig.1.Both inner and outer shapes of sophisticated composite rotor blades can be simultaneously investigated to generate optimal rotor blades in terms of aerodynamic performance,structure,and manufacturing cost.

The framework initially sizes the whole configuration of a helicopter at the preliminary level.At this step,the rotor blade planform is assumed to be rectangle,and its radius and chord length are consequently specified.The rotor blade’s configuration including the airfoil shape and the rotor blade planform(twist,taper ratio,position of taper,and chord length)is then identified in the aerodynamic analysis loop.

A new geometry representation algorithm which uses the class function/shape function transformation(CST)method is applied to consider the airfoil shape.The advantages of this CST method are high accuracy and use offew variables in geometry representation.20

A good design of rotor blades requires not only good performance but also a good structure and dynamics behavior.The inner structural configuration needs to be designed to ensure that the rotor blade will work properly.

The manufacturing factor mentioned previously should be considered at an early state of the design to improve the competitiveness of products in the marketplace,so a modular manufacturing is implemented and integrated with other modules to fulfill the design process.

The airfoil shape governed by a new geometry representation method—CST is considered parallel with other outer configuration of rotor blades(tapper ratio,twist,position of tapper,and chord)and inner structural con figuration(D-spar thickness,skin thickness,web position,and orientation of each composite layer).In addition,the manufacturing factor can be considered at an early state of design together with aerodynamics and structure factors.

2.1.Aerodynamic analysis

2.1.1.Airfoil characteristic analysis

Airfoil shape plays an essential role in helicopter performance.However,it used to be considered in separate design optimization.The aerodynamic module is implemented for rotor blade performance analysis where the rotor blade planform and the airfoil are considered at the same time.In helicopter performance analysis,the airfoil characteristics are usually represented in a C81-table format where lift,drag,and moment coefficients of the airfoil are predicted for subsonic to transonic flow and a wide range of angle of attack(AOA).In this framework, diverse methodologies (the Navier-Stokes equation-solving method,the high-order panel method,and Euler equations solved with the fully coupled viscous-inviscid interaction method)are employed.21The sequential applications of each method are as follows:

Fig.1 Integrated framework for helicopter rotor blades design.

(1)A high-order panel with the fully coupled viscousinviscid interaction method for Ma∞≤ 0.4.

(2)The Euler equations solved with the fully-coupled viscous-inviscid interaction method for 0.4＜Ma∞≤0.7.

(3)The 2D Reynolds averaged Navier-Stokes(RANS)equation-solving method for Ma∞＞0.7.

The 2D RANS method is only used for Ma∞＞0.7 when the two less expensive methods(Euler equations and the high-order panel solved with the fully coupled viscousinviscid interaction method)are less suitable.

By integrating commercial software and in-house codes,a fully automated process has been developed for generating C81 tables quickly and accurately for arbitrary airfoil shapes.

There are many factors affecting the total time to generate a C81 table.21These factors include the number of cases(Ma∞and AOA(AoA pairs)),the speed of processors,grid systems,flow solver models,and the duration of the longest case.The longest computational time is required by the RANS method.Thus the treatment of the conditions when the RANS method is applied has a very important role in reducing the computational time.The initial calculation using Fluent software requires 300–500 iterations while the proceeding calculations require 100–200 iterations to be converged.Each iteration requires about 0.4 s on a computer having a dual-core,2.5 GHz CPU with 3.00 GB of RAM.The solving panel and Euler equations with viscous/inviscid interaction method require a little time less than 5 s for a pair of AoA and Ma∞.The computationally expensive RANS method is only applied for Ma∞＞0.7.This advance makes the process applicable for design purposes,where the designers seek to update their airfoil tables frequently for new designs.Validated results of the process are shown in Ref.21.Agreements between calculated results and experimental data are obtained.

The airfoil is represented by the CST method.

The airfoil distribution functions defined as upper and lower curves are presented sequentially as22

where AU0,AU1,AU2,AU3and AU4are the variables of the upper curve of the airfoil distribution function;AL0,AL1,AL2,AL3and AL4are the variables of the lower curve of the airfoil distribution function;and x and y are the airfoil coordinates

2.1.2.Helicopter performance analysis

Konkuk Helicopter Design Program(KHDP),a helicopter sizing,performance,and trim analysis program,was developed at Konkuk University.These codes were developed for use in the conceptual design phase and hence they used empirical formulas to reduce computing time.

Blade element theory(BET)was implemented to calculate the required power in different helicopter operations,namely hover,climb,cruise,descent,and autorotation.BET needs to call trim module analysis to obtain the required power.Therefore,the required power is a function of the airfoil shape and the blade planform.

Validated results of each module are shown in Ref.18.The differences between calculated results and existing data are within 5%in general,hence acceptable for the preliminary design phase.

2.1.3.Aerodynamic design module

The development of a sizing,performance analysis program and the automated generation of airfoil characteristics enable a design optimization study of helicopter rotor blades.The integrated framework for aerodynamic design optimization is wrapped in ModelCenter and shown in Fig.2.

The NACA0012 airfoil is chosen for the first step of a design process.Then,blade shapes such as chord distribution,twist distribution,and airfoil coordinates are generated.The required power is computed by performance analysis and the trim condition is checked.The blade element method is used to calculate the required power in order to consider the airfoil characteristics.Some other additional codes to generate airfoil coordinates,chord distribution,and twist distribution are implemented in order to build a full framework for the optimization process in ModelCenter.

2.2.Structural analysis

This section will describe the automated process for helicopter rotor blades’structural design.

The cross-sectional template consists offour components:a leading cap,a D-spar,a skin,and a web as shown in Fig.3.The leading cap and the web are always adjacent to the D-spar.As the web’s position moves along the chord spanwise and the airfoil shape changes,the D-Spar and the web automatically adjust to fit inside the airfoil.The leading cap is assumed to be made of titanium for anti-erosion purpose.Other components such as the D-spar,the web,and the skin are made of the continuous IM-7/PEEK composite material.

2.2.1.Sectional properties analysis

High-fatigue characteristics and a high stiffness/weight ratio of composite materials lead to a wide use in the design of helicopter rotor blades.

Fig.2 Integrated framework in ModelCenter for aerodynamic design optimization.

Fig.3 Structural baseline model.

Helicopter rotor blades are generally modeled as initially curved and twisted anisotropic beams.In this study,the sectional analysis of composite blades is conducted by VABS(variational asymptotic beam sectional analysis)software.VABS is capable of modeling initially curved and twisted,nonhomogeneous anisotropic beams with arbitrary cross-sectional configurations.VABS is a code implementing various beam theories based on the concept of simplifying the original nonlinear 3D analysis of slender structures into a 2D crosssectional analysis and a 1D nonlinear beam analysis using a powerful mathematical method,the variational asymptotic method.23

VABS takes a finite element mesh of the cross section including all the details of geometry and material as an input to calculate the sectional properties including structural and inertial properties.24Chen and Yu25developed PreVABS(pre-processing of VABS),a design-driven pre-processing computer program,which can effectively generate high-resolution finite element modeling data for VABS by directly using design parameters and both the span-wisely and chord-wisely varying composite laminate lay-up schema for rotor blade and aircraft wing cross-sections.

However,the robustness of PreVABS has not been achieved.The layers at the leading edge may intersect each other when the curvature becomes high.A mesh cannot be created in some critical cases when the airfoil shape is changed significantly.Especially,PreVABS cannot generate a mesh for arbitrary values of the D-spar and the skin number of layer;hence it restrains the choice of design variable as shown in Ref.17.Moreover,the airfoil coordinates may not be compatible with PreVABS to generate a mesh.The input data used to be manually adjusted by designers.Because of these reasons,several analytical tools were implemented to automatically fulfill the process as shown in Fig.4.

The Intersect program analyzes the data of airfoil coordinates and creates an input file to run the PreVABS program where the ‘no intersection point” problem at the tailing edge and ‘offset intersection” at the leading edge are avoided.Pre-VABS will generate connectivity of elements for an insufficient model as shown in Fig.5.

Fig.4 Implemented processforcross-sectionalproperties analysis.

Additional mesh points which the PreVABS program is not able to generate will be provided by the lepots program as shown in Fig.6.The lepots program reads the output data from PreVABS and then creates the input,a process to generate additional mesh points for the deficient part of the original cross-sectional mesh.

The meshes at the tailing edge,the web,and the skin intersection are analyzed and regenerated for a realistic structure as shown in Fig.7.

After creating the additional mesh,the lepots program reads the data from PreVABS’s and Gridgen’s outputs in order to generate input files of the VABS program.The input files present the connectivity and information of elements for a sufficient model.

2.2.2.Integrated aerodynamic and structural data transfer program

A program,TRIMFST,is implemented to construct the flow condition(Mach number and AOA)corresponding to elements of rotor blade data for cross-sectional aerodynamic analysis at a trim condition.The trim angles are used for aerodynamic analysis of the cross-section at a certain flight condition.A program,Afluente,performs aerodynamic analysis at the given cross-section to calculate the pressure at each airfoil coordinate.

2.2.3.Stress analysis of a 3D rotor blade

The 1D beam analysis is replaced by a 3D model in ANSYS with a static force applied on a beam.The analytical procedure is automated using the tool command language(Tcl)of ANSYS as shown in Fig.8.

Fig.5 Insufficient model for leading edge of an airfoil section.

Fig.6 Additional mesh points for leading edge of an airfoil section using Gridgen.

Fig.7 Intersection mesh after processing.

A program named Ansysin is implemented to transfer the aerodynamic data from Afluente to the structural model in ANSYS software.Afluente also writes the Tcl commands to automatically generate a structural analysis model including key points,lines,surfaces,mesh,materials,composite stacking layers,boundary condition,applied pressure,analysis solver,failure criteria,and safety factors.

2.2.4.Structural module

The whole structural modules are wrapped in ModelCenter as shown in Fig.9.

Several codes are used to check timeout and control parallel running of analysis.

The sensitive analysis will show the effects of design variables on the objective function and examine the integration of the framework shown in Fig.10 as well.The structure is strengthened when the D-spar,web,and skin number of layer increase.The Tsai-Wu index values(Eq.(8))then decrease.The dynamics and structure of the section are enhanced when the web position moves toward the tailing edge.Increasing the number of layers of the spar,the skin,and the web is also a way to strengthen the structural performance.However,these could make manufacturing cost go up.Therefore,the design of rotor blades has to consider structural performance in conjunction with manufacturing cost in order to acquire reality.The sensitive analysis shown in Fig.10 expresses that the framework works properly in this study.

Fig.9 Structural design framework in ModelCenter.

2.3.Rotor blades manufacturing cost estimation

2.3.1.Manufacturing cost and system performance analysis

Fig.8 Automated process in ANSYS for stress analysis.

Fig.10 Sensitive analysis of structural design variables.

An integrated model for composite rotor blade manufacturing cost estimation has been developed at the Aerodynamic Analysis and Design Laboratory(AADL),Aerospace Information Engineering Department,Konkuk University.The model for estimating manufacturing costs is based on an understanding of the inherent relations between product design,process flow,and product costs.Once the configuration and geometric size of a part,manufacturing technique,and material are selected,the detailed process flow can be divided into smaller sub-steps.These sub-steps depend on the objective of the cost model and the information available.26

As an example,COSTRAN®code,which is for commercial process-based manufacturing and assembly cost(PBMAC),was applied by Bao and Samareh27for multidisciplinary design optimization(MDO)application.Several modelsand approachesevaluating manufacturing costsfor composite products have been presented in the literature.28Most of the costing approaches are either process-specific thus limited in application,or require complicated computer-based systems.Manufacturing cost estimates are generated without consideration of the process-performance-cost interrelation as pointed by Bernet et al.28who developed an integrated cost and consolidation model for commingled yarn-based composites.Our approach has the same objective but a different composite application process.In this study,a manufacturing cost estimation model is incorporated to our MDO problem.For simplicity,the model focuses on manufacturing cost.An activity-based costing approach is applied in our model following the composite manufacturing flow.The manufacturing cost of composite materials includes material cost,labor cost,equipment cost,and tooling cost,which are related to the process time.The time estimate is based on the manufacturing process.26The material cost is calculated for each process activity listed in the process plan.The quantity of a material used is calculated from the size parameters and description of the material.The quantity is multiplied by the unit cost for that material obtained from an inventory database.Individual items are then summed for the total material cost of the product.Labor cost is calculated for each process activity listed in the process plan.For each activity/process time,the cost of a labor resource consumed is calculated by multiplying the time by the cost rate for the labor resource that is obtained from an employee code rate database.Individual items are then summed for the total labor cost included in the product.The equipment activity cost is calculated using the direct process activity rate multiplied by the machine cost rate.The machine cost rate for each production machine is calculated based on maintenance costs,operating cost,equipment asset,and the number of operation hours.For each activity/process time,the cost of an equipment resource is calculated by multiplying the job time with the cost rate for that equipment resource.26

In this study,integrated models are implemented to provide a rapid and dynamic feedback for a designer or a product development team who performs manufacturing cost estimation and system performance evaluation to manufacture a new or existing product during early design processes.

2.3.2.Manufacturing cost module

This module is wrapped in ModelCenter.Sensitive analysis will show the effects of design variables on the objective function and examine the integration of the framework.

The sensitive analysis of design variables on aerodynamics and structure analysis have been shown previously.This section will show the sensitive analysis of design variables on the manufacturing cost;thereby,it will demonstrate the integration of the framework from aerodynamic analysis to structural analysis and manufacturing cost estimation.

A more twisted and shorter taper rotor blade requires more processing time and materials,hence this increases the manufacturing cost.The rotor blade planform could vary the manufacturing cost up to 15%as shown in Fig.11.

Airfoil shapes slightly influence the manufacturing cost as shown in Fig.12.An asymmetrical airfoil requires a higher cost to be manufactured.The manufacturing cost varies within 1%,so we can fix the airfoil shape to simplify the problem.Airfoil shape is not considered as a design variable in integrated design optimization.

The structural design requires a thicker D-spar,skin,and web while manufacturing requires less material and complexity.The manufacturing cost could vary by 5%in a tentative range of structural design variables as shown in Fig.13.

The airfoil shape has an important role in aerodynamic performance but a slight effect on structure and manufacturing cost.Therefore,the airfoil shape could be designed in advance to reduce computational time,and then fixed for the next design loop where both planform and inner structures of rotor blades are simultaneously considered for multidisciplinary design optimization.

3.Integrated aerodynamics and structure design optimization considering manufacturing cost

This section describes an integrated framework including aerodynamics,structure,and manufacturing cost.All inner and outer shapes of rotor blades can be investigated simultaneously in a fully integrated design optimization.The purpose of this article is to demonstrate the completed framework,so the design optimization is performed in an efficient process.The airfoil shape much affects aerodynamic performance of a rotorcraft while its effect on the structure is less.Therefore,the airfoil shape is first considered in conjunction with the planform in aerodynamic design optimization which is shown in Section 3.1.The airfoil shape variables are then fixed while the planform design variables still need to be investigated in the next integrated design optimization of aerodynamics,structure,and manufacturing cost as shown in Section 3.2.

3.1.Aerodynamic design optimization

This design process starts with the sizing module.A rectangular blade will be defined by the sizing module.This blade shape will be a baseline shape for the next step of the optimization design process.

Fig.11 Sensitive analysis of blade planform on manufacturing cost.

Fig.12 Sensitive analysis of airfoil shape on manufacturing cost.

Fig.13 Sensitive analysis of inner structure on manufacturing cost.

Airfoil analysis is performed by an automated process to generate airfoil aerodynamic characteristics in a C81 format describing lift,drag,and moment coefficients with respect to Mach number and AoA.Some other additional codes to generate airfoil coordinates,chord distribution,and twist distribution are implemented in order to build a full framework for the optimization process in ModelCenter software which is a powerful tool for automating and integrating design codes.

Using the integrated framework,both the blade planform and the airfoil shape are considered simultaneously in the design optimization.The sensitivity analysis of design variables and design optimization were investigated in Refs.22,29.The analysis also addresses to the fully automated process of aerodynamic design and analysis.Table 1 summarizes the aerodynamic design optimization problem solved by Refs.22,29.

In a hover case,we can see that the optimum taper ratio and position of the taper are on the boundaries of these design variables.These results match the optimum hovering rotorwhich requires the local chord distribution over the blade to be given by

Table 1 Design optimization investigated by aerodynamic module.

The local blade chord must vary hyperbolically with span and can be adequately approximated by a linear taper over the outer part of the blade.Therefore,each section of the blade operates at an optimum lift-to-drag ratio.

The optimum blade shape has a smaller solidity in comparison with the baseline.In this case,the twist decreases from-8°to-15.3°in order to compensate lift reduction due to a smaller solidity.The optimum blade planform could generate uniform inflow from the taper position to the tip,hence minimizing the induced power.The optimum airfoil shape has a higher thickness and camber compared to the baseline,thereby increasing the maximum lift of the airfoil.We can easily see that with the optimum taper,twist,and airfoil shape,values of the local lift coefficient decrease at the blade root and increase at the tip.This reduces the profile power component,so the rotor can be operated at the same thrust but with an improvement offM.The optimum results in which the required hover power decreases by 7.4%and FM increases by 6.5%are good values for rotor blade design.

In forward flights,the maximization of the drag divergence Mach number leads to a reduction of the thickness and camber of the airfoil.In contrast,the reduction of the thickness and camber of the airfoil can reduce the maximum lift characteristics and cannot avoid premature trailing edge separation.

The optimal airfoil in 120 kt(1 kt=1.852 km/h)forward flight design optimization has a smaller thickness and camber compared to those in a hover case.The drag could increase signi ficantly at the advancing side in 120 kt flights,so the camber and thickness should be reduced.The compromise between drag and lift coefficients leads to a reduction in the camber and thickness as well.The rotor blade solidity in 120 kt flights does not change much in order to provide enough thrust.A small taper at the tip could reduce the drag on the advancing side.

The objective function is reduced by 4.4%after the design optimization process.The FM increases by 4.3%.The required power in 120 kt forward flights is reduced by 5.3%.However,the airfoil characteristics are improved to the desired ranges of lift,drag,and moment coefficients which are very important in rotor performance.

3.2.Integrated aerodynamics and structure design optimization considering manufacturing cost

The airfoil shape is fixed and taken from the design optimization study for forward flights in order to reduce the computational time.Design optimization results of the airfoil shape have been solved in Ref.29and are repeatedly shown in Table 2.

The sectional properties of the baseline layout are shown in Table 3.

3.2.1.Objective function

The cross-section design problem is proposed to determine the values of all design variables including cross-sectional stiffness and inertia constants so as to satisfy chosen constraints andminimize a chosen objective function.In order to improve the payload of an aircraft,the rotor blade mass per unit length m is generally expected to minimum.The cross-section design must guarantee bending and torsional stiffnesses to be in a desired range to avoid resonance.The dynamic coupling of bending and torsional loads is very important because it is responsible for flutter and other dynamic instabilities in rotor blades.The coupling depends on the lift(a transverse load)and the distance e between the SC and the AC.Hence,the cross-section design attempts to minimize the distance between the SC and the AC as well as the distance d between the MC and the AC for similar reasons.Moreover,the structure must perform without a failure under specified service loads.Whether or not a failure occurs is measured by the Von Mises criterion for isotropic materials and the Tsai-Wu criterion for anisotropic materials.

Table 2 Optimal values of design variables at 120 kt forward speed flights.29

Table 3 Sectional properties of baseline layout.

The objective function of the integrated design optimization shown in Eq.(4)is to minimize a combination of aerodynamics,structure,and manufacturing cost values using weight factors,denoted wa,ws,and wc.An isolated objective function for each discipline was discussed in Refs.17,22,29.The value of the objective function for a rotor blade baseline configuration is 1.

In this study,the aerodynamics and structure are weighted at the same level(wa=0.4 and ws=0.4).The weight factor of manufacturing cost is wc=0.2.These weight factors mean that the aerodynamics and structure characteristics dominate the manufacturing cost.Moreover,designers can easily set up these weight factors according to their own requirements.

3.2.2.Design variables

The airfoil shape is fixed in order to reduce computational time.The airfoil shape is chosen from aerodynamic design optimization in a 120 kt forward flight condition.

Current design optimization is a nonlinear optimization problem with a mix of continuous and discrete variables.Design variables are planform(taper ratio,position of taper,and root chord length),pre-twist,and inner configuration(web position and number of layers of D-spar,web,and skin).The fiber orientations are discrete variables.They could be design variables.The composite layer thickness is usually a constant for a product due to manufacturing cost,so it is fixed for all components of rotor blades.This leads to many layers of D-spar,web,and skin.Therefore,the orientations offibers are fixed in order to reduce the number of design variables.This assumption does not debase the framework because the main difficulties are the considerable changes of inner and outer configurations of rotor blades.The fiber orientations of D-spar are assumed to follow the 0/45/-45 sequence,while those of web and skin follow the 45/-45 sequence.

3.2.3.Constraints

Mass per unit length of the optimal cross-section is no more than that of the baseline:

The stress level of the optimal cross-section is less than that of the baseline:

For composite materials,the safety factor g is defined by Tsai-Wu failure criterion as

where Xt,Yt,Xc,Yc,and S are the ultimate tension,compression stresses,and shear stress of unidirectional laminated materials,respectively. σ1, σ2,and τ12are the stresses along the two material directions and the shear stress,respectively.The inverse safety factor 1/g with the Tsai-Wu failure criteria,similar to Von Mises stress normalized by the ultimate strength,indicates a dangerous level locally.

The sectional stiffness of the optimal cross-section is in the range of-5%to+10%of the baseline values:

The centrifugal force is an important force acting on a rotor blade.Dynamic analysis could not be considered in the current framework.Only static structure design was considered.The centrifugal force could be decomposed into 2 force components(FCXand FCZ).FCZworks as damper of the aerodynamic force.FCXacting on the rotor spanwise direction may make the structure broken.An additional constraint is made in this direction to ensure that the blade will not be broken due to the centrifugal force,which is the blade spanwise stiffness coefficient S11(generalized Timoshenko stiffness matrix)for X direction:

The effects of coupling terms on the rotor blade aeroelastic response have not been investigated.Therefore,several constraints of coupling stiffness are made.The coupling stiffnesses of extension-twist and bending-twist are far smaller than the stiffness they couple:

The performance of the optimal blade planform is better than that of the baseline:

The trim condition is attainable with any rotor blade planform:

The production rate of the manufacturing process is more than 200:

The feasible values of nondimensional design variables and constraints are summarized in Table 4.

3.3.Optimization method

The Darwin tool in ModelCenter is employed to find the optimal solution.The genetic algorithm(GA)method is used in this tool.

The current design optimization is a nonlinear optimization problem with a mix of continuous(blade planform design variables and web position)and discrete variables(number of layers of D-spar,skin,and web).

The inputs of the GA method are summarized in Table 5.

3.4.Optimization results

Optimization results are shown in Table 6.Fig.14 shows optimal shape of rotor blade.Convergence history of the objective function(Fig.15)shows success of the framework.The chord length does not change much compared to the baseline.The arrangement of the inner structure can increase the stiffness of the cross-section in general.

The taper position moving toward the blade root is at 0.53 rotor radius.This could slightly worsen forward flight performance of a helicopter in comparison with the optimized blades for 120 kt forward flights obtained in Table 2.However,this could reduce the rotor blade weight and the manufacturing cost which are other targets of the design problem.The main purpose of this compromise is to improve multidisciplinary objectives including aerodynamic performance,structure,and manufacturing cost,so some factors could be worse respectively.The aerodynamic performance of rotor blades in hover flights is required not less than that of the baseline.The chord length,taper position,taper ratio,and twist are critical design variables describing aerodynamic performance,so the optimization results in 0.7 offM.The more rotor blades are twisted,the higher the manufacturing cost is.This leads to a decrease to 10°of twist compared to 13 in isolated forward flight design optimization.

All extension-twist and bending-twist coupling terms are far smaller than 0.01 to ensure that the resonance is avoided.The number of layers of D-spar is signi ficantly reduced to 25 layers,so the torsional stiffness of the structural section is worse.However,the web position moves toward the tailing edge of the blade to compensate the torsional weakness due to a thinner D-spar,while the material and labor costs can be reduced.The torsional stiffness is retained at 95%of the baseline.The distance between the SC and the AC is-0.28%chord length;the distance between the MC and the AC is 12.4%chord length;the mass length is not changing much with a-1%reduction.We can see that the distance between the SC and the AC decreases while the distance between the MC and the AC increases.However,the combination function of the structure is much reduced due to theweight factor.The objective function is reduced by 9%.In this study,the non-structural mass is not considered in the design problem.It is reasonable because this mass is usually used to adjust the MC and autorotational inertia of a rotor blade in reality.

Table 4 Nondimenional constraints and design variables values.

Table 5 GA optimization parameters.

Table 6 Optimization results nondimensionalized by baseline values.

Fig.14 Optimal rotor blade.

Fig.15 Convergence history of objective function.

4.Conclusion

This study developed an integrated framework for rotor blades design optimization.The framework is constructed by three main modules which are sizing and aerodynamic performance analysis, structure analysis, and manufacturing cost estimation.

The aerodynamics module starts with the sizing of a helicopter based on customer requirements.After the sizing,the rotor blades of the helicopter will be designed regarding aerodynamics,structure,and manufacturing aspects.

A number of aerodynamic and structural programs were developed and wrapped in ModelCenter.The validation of each program show that the uses of them are suitable for current design phase.

The airfoil analysis tool effectively automates the generation of airfoil characteristics tables where lift,drag,and moment coefficients of the airfoil are predicted for subsonic to transonic flow and a wide range of attack angle.Diverse methodologies(the Navier-Stokes equation-solving method,the high-order panel method,and Euler equations solved with the fully coupled viscous-inviscid interaction method)are employed.This tool enabled the ability to simultaneously consider both the rotor blades planform and the airfoil shape in a design optimization.

A modular structural design methodology was developed for composites rotor blades.All inner components such as the D-spar,the skin,and the web are parameterized.A number of codes were implemented to automate the structural analysis from processing of the aerodynamic data to sectional properties and stress analysis.

By integrating the manufacturing cost estimation module,manufacturing factors can be considered at an early stage of design along with aerodynamic performance and structure simultaneously.

Acknowledgements

This work was supported by the National Foundation for Science and Technology Development(NAFOSTED)of Vietnam(No.107.04-2012.25).

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Ngoc Anh Vu received his B.S.degree in aerospace engineering from Ho Chi Minh City University of Technology in 2006.He then received his Ph.D.degree from Konkuk University,Seoul,Korea in 2012.He is currently an instructor at Ho Chi Minh City University of Technology in Ho Chi Minh City,Vietnam.He is also a partner of the Institute for Computational Science(INCOS)at Ton Duc Thang University,Ho Chi Minh City,Vietnam.His research interests include aerodynamic design and optimization,multidisciplinary optimization,and aerospace vehicle design.

Jae Woo Lee received his B.S.and M.S.degrees in aerospace engineering from Seoul National University in 1984 and 1986,respectively.He then received his Ph.D.degree from Virginia Polytechnic Institute and State University in 1991.Dr.Lee is currently a professor in the School of Aerospace Information Engineering at Konkuk University in Seoul,Korea.He serves as an editor of the Journal of Korean Council on System Engineering,KCOSE.Dr.Lee’s research interests include aerodynamic design and optimization,multidisciplinary optimization,aerospace vehicle design,computational fluid dynamics,and e-manufacturing.

Tuan Phuong Nam Le received his B.S.degree of mechanical engineering from University of Technology,Ho Chi Minh City,Vietnam in 2000.He then received his Ph.D.degree in computational hypersonic aerodynamics from the Department of Mechanical Engineering at University of Strathclyde,Glasgow,United Kingdom in 2010.He is currently an instructor in the Department of Mechanical Engineering at Industrial University of Ho Chi Minh City,Vietnam.His research interests include computational fluid dynamics,hypersonics,and nano/microscale rarefied gas flows.

Song Thanh Thao Nguyen received her B.S.degree in aerospace engineering from Ho Chi Minh City University of Technology in 2009.She then received her Ph.D.degree from ENSMA University,France in 2013.She is currently an instructor at Ho Chi Minh City University of Technology in Ho Chi Minh City,Vietnam.Her research interests are composite material and structural design.

2 September 2015;revised 12 November 2015;accepted 29 August 2016

Available online 17 October 2016

*Corresponding author.Tel.:+84 91 8340297.

E-mail addresses:vungocanh@tdt.edu.vn(N.A.Vu),jwlee@konkuk.ac.kr(J.W.Lee),nam.tp.le@gmail.com(T.P.N.Le),nguyensongthanhthao@gmail.com(S.T.T.Nguyen).

Peer review under responsibility of Editorial Committee of CJA.

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http://dx.doi.org/10.1016/j.cja.2016.10.001

1000-9361Ⓒ2016 Chinese Society of Aeronautics and Astronautics.Production and hosting by Elsevier Ltd.

This is an open access article under the CC BY-NC-ND license(http://creativecommons.org/licenses/by-nc-nd/4.0/).

Design optimization;

Helicopter rotor blades;

Integrated framework;

Modular structure design methodology;

Perform estimation

Ⓒ2016 Chinese Society of Aeronautics and Astronautics.Production and hosting by Elsevier Ltd.This is anopenaccessarticleundertheCCBY-NC-NDlicense(http://creativecommons.org/licenses/by-nc-nd/4.0/).