Mechanics of Solids Final Project:

ANSYS Analysis of Helicopter Main Rotor Airfoil

Authors:

Terry Yu

December 16, 2016

Swarthmore College, Department of Engineering

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Table of Contents

Abstract ......................................................................................................................................................... 2

Introduction ................................................................................................................................................... 3

Project Objectives ......................................................................................................................................... 4

Theory: Airfoils ............................................................................................................................................ 5

Theory: Materials and Isotropy ..................................................................................................................... 6

Theory: Finite Element Analysis .................................................................................................................. 7

Procedure ...................................................................................................................................................... 7

Model: SolidWorks ....................................................................................................................................... 8

Model: ANSYS Workbench ......................................................................................................................... 8

Results ........................................................................................................................................................... 9

Discussion ................................................................................................................................................... 11

Conclusion .................................................................................................................................................. 12

References ................................................................................................................................................... 12

Appendix A: ANSYS Outputs .................................................................................................................... 14

Appendix B: Final Presentation .................................................................................................................. 21

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Abstract

The objective of this project was to construct a 3D model of a helicopter main rotor

airfoil and conduct a structural analysis while subjecting it to various wind loads. This was

achieved with a simple extruded model of the NACA 0012 airfoil that was built in SolidWorks

and imported into ANSYS Workbench. This airfoil was created to be 0.9 meters in width and 7.5

meters long. The model was pinned on one end and simulated as rotating around an imaginary

hub, and was subject to the relevant centrifugal and aerodynamic forces. Lift and drag forces

were simulated with a simplified equation and previously determined lift and drag coefficients.

The resulting model showed a reasonable deformation, as well as revealing principal stress, Von

Mises stress, and maximum shear stress data. This was an accurate, if simplified simulation of a

main rotor blade, but laid the ground for further and more complete characterization of this

model.

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Introduction

Helicopter blades operate at a mechanically interesting region of the aircraft. Responsible

for the entire weight of the helicopter, they are subject to enormous aerodynamic and structural

stresses, making their construction critical to the longevity and endurance of the helicopter.

Materials science has brought forth many advancements to the field of helicopter blades. From

the earliest blades made of wood, to the metal blades of the mid-century, to the composite blades

of today, the construction of this pivotal piece of hardware has changed significantly over time.

Figure 1: Composite Construction of Blade [1]

The physics behind the blade, however, remain largely the same. The blade is subject to

lift, drag and centrifugal forces. These vary with radius from the blade hub, and subsequently

analyses are aided by computer simulation. It is of great interest to examine potential failure

modes and deflections of blades, as failure of the blade is often catastrophic to the vehicle. This

analysis does not examine the potential scenarios in which a blade may fail, but merely analyzes

it in an ideal hovering situation.

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Project Objectives

For this ENGR059 project, an extruded airfoil will be examined using ANSYS

Workbench under steady state conditions. ANSYS Workbench was used instead of using

ANSYS APDL directly as it was capable of varying pressure loads with direction, something

that required a complex workaround in ANSYS APDL. ANSYS Workbench is also a more

modern piece of software, and integrates will with other ANSYS packages, such as FLUENT for

fluid analysis.

This analysis will focus on the blade for an idealized hovering helicopter, and consider

the centrifugal, gravity, drag, and lift forces on the helicopter blade. This analysis was done at

three varying speeds, to simulate a range of conditions. The stresses involved will be analyzed

and a qualitative evaluation of the blade forces will be made. The model is not of sufficient

fidelity that it would be useful in its current state; however, there are some refinements that can

be taken to turn this into a more accurate representation of a real blade. Currently, the aim of this

project is to gain proficiency in using this software and facilitate future analyses. In addition, it

combines my fluid dynamics and mechanics background, making for an interesting project.

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Theory: Airfoils

The significant forces acting on a helicopter blade are lift, drag, and the centrifugal force.

Gravity is not shown below, and contributes relatively to the stresses on a blade in flight. Lift

and drag are generated by the blade in the course of normal flight. The factors that detail exactly

the amount of lift and drag generated are the topic of intensive aerodynamic study, but for the

purposes of this analysis the lift and drag can be approximated as follows:

𝐹𝐿 =1

2𝜌𝑣2𝐴𝐶𝐿 𝐹𝐷 = −

1

2𝜌𝑣2𝐴𝐶𝐷

In these expressions, 𝜌 is the density of the air, 𝑣 is the velocity of the blade relative to still air, A

is the area exposed to the air, and 𝐶𝐿 and 𝐶𝐷 are coefficients of drag and lift, respectively. These

relations are empirically determined.

Figure 2: Helicopter Blade Forces

For this analysis, I used the NACA 0012 airfoil. This is a widely studied and publicized

airfoil for helicopters, and has good general performance characteristics.

Figure 3: NACA 0012 Airfoil

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From various NASA tests, empirical numbers have been determined for 𝐶𝐿 and 𝐶𝐷 . Due to the

ubiquity of the NACA 0012 airfoil, much data is available for its performance, and it is favored

in use for simulation verification. [2]

Figure 4: Graphs relating alpha, 𝑪𝑳, and 𝑪𝑫 [2]

To simplify the analysis, an angle of attack of 10° was chosen, so that the coefficient of lift was

one. The corresponding coefficient of drag was chosen. These numbers are considered a good

enough first approximation, as the focus of this project was structural and not aerodynamic.

Theory: Materials and Isotropy

For the analysis, the blade was assumed to be composed of isotropic carbon fibre

composite. As shown earlier, blade construction is very complex these days, and often consists

of multiple metal spars reinforced with a composite construction and wrapped in sheets of

polycarbonate or other protective material. For this analysis, the Young’s Modulus was set to

300 GPa, consistent with the most high strength of composites. [3]

Though the assumption of isotropy is not a very accurate one, the resulting model was

fairly consistent with observed performance of helicopter blades. Since many blades are hollow

or are filled with non-structural materials, it may be that the effects of these spaces cancel out

with the stronger materials used in actual blade construction.

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Theory: Finite Element Analysis

Finite element analysis is the standard for conducting these computational analyses. By

subdividing the larger model into smaller pieces, equations can be developed that characterize

the interaction between these pieces. With known material properties, loads, and restraints, a

structural analysis can be numerically approximated where an analytical solution may be

impractical or impossible. The accuracy of the results is highly dependent on the techniques and

assumptions used in the modeling, however.

For this analysis, ANSYS workbench obscures the modeling method more than ANSYS

APDL. It appears to use an adaptive mesh to save computational resources and refine only where

needed. For this reason, it is difficult to talk about the explicit methods employed by the

elements, as they will change from model to model and are not quite as exposed to the end user.

Procedure

1. Develop theories for aerodynamic forces

2. Research material properties of blade

a. Young’s Modulus: 300 GPA

b. Density: 1830 kg/m3

3. Develop model in Solidworks

4. Export model to ANSYS Workbench

5. Set boundary conditions and apply forces

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Model: SolidWorks

The outline of a NACA 0012 airfoil was obtained, and then extruded into an airfoil in

SolidWorks 2015. The airfoil is 0.9m wide and 7.5m long.

Figure 5: SolidWorks Airfoil Extrusion

Model: ANSYS Workbench

From there, the model is imported into ANSYS Workbench and the appropriate forces

are applied. Gravity is not depicted here, as it was in a separate category of forces.

Figure 6: ANSYS Workbench Model with Forces

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Results

Figure 6: Summary of Deformation for Stress Analysis

Figure 7: Summary of Von Mises Stress for Stress Analysis

0

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

0 10 20 30 40 50 60

Def

orm

atio

n (

m)

Rotation (rad/s)

Max Deformation

0.000E+00

2.000E+08

4.000E+08

6.000E+08

8.000E+08

1.000E+09

1.200E+09

1.400E+09

1.600E+09

1.800E+09

0 10 20 30 40 50 60

Vo

n M

ises

Str

ess

(Pa)

Rotation (Rad/s)

Max Equivalent Stress (Von Mises Stress)

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Figure 8: Summary of Shear Stress for Stress Analysis

Figure 9: Summary of Principal Stress for Stress Analysis

0.000E+00

1.000E+08

2.000E+08

3.000E+08

4.000E+08

5.000E+08

6.000E+08

7.000E+08

8.000E+08

9.000E+08

1.000E+09

0 10 20 30 40 50 60

Shea

r St

ress

(P

a)

Rotation (Rad/s)

Max Shear Stress

0.000E+00

5.000E+08

1.000E+09

1.500E+09

2.000E+09

2.500E+09

0 10 20 30 40 50 60

Pri

nci

pal

Str

ess

(Pa)

Rotation (Rad/s)

Max Principal Stress

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Rotation (Rad/s) 50 35 20

Max Deformation (m) 1.3576 0.6652 0.2172

Equivalent (Von Mises Stress) (Pa) 1.701E+09 8.333E+08 2.721E+08

Max Principal Stress (Pa) 2.050E+09 1.004E+09 3.279E+08

Max Shear Stress (Pa) 9.517E+08 4.663E+08 1.523E+08

Table 1: Maximum stresses for select rotation speeds

Figure 10: Representative Von Mises Stress Distribution

Discussion

The results are consistent with expected predictions on deflection of the helicopter blade.

As expected, the greatest stresses are at the base of the rotor. There is an obvious and expected

nonlinear trend in the stresses, as the lift and drag force increase quadratically with speed. The

deflection of 1.36 meters at the highest speed was a large amount. Recent work at NASA Ames

suggests that a deflection of up to 30 inches is expected in normal flight, so there are clearly

inaccuracies in our model.[4] The largest suspect is our very simplified aerodynamic loads. The

simple relationship between lift and drag becomes very complex quickly in a rotating system,

and a more complete analysis with FLUENT would be useful in determining a result with more

accuracy to experimental results. In addition, this model assumes still air. Helicopters moving at

a significant speed mean that ½ of the time, the blades are rotating in the direction of travel and

thus encounter higher wind speeds and correspondingly higher stresses.

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Our model’s lack of internal structure also contributes to inaccuracies. With a reinforcing

metal inside or stiffer materials, it is likely that the deflections would be lessened. However, the

extrusion model has been verified, and while a few of my predecessors modeling in ANSYS

have had some issues with element limits, the newer software in ANSYS Workbench and the

adaptive elements seems to be capable of modeling in full 3D elements and not shells, which is

an improvement in fidelity. With further development time, it is possible to develop the model

with an accurate internal structure and examine the interactions that go on when that blade is

summarily stressed.

Conclusion

This project underwent a 3D aerodynamic stress analysis of a helicopter blade. It was a

useful introduction to the use of SolidWorks and ANSYS, as well as revealing many of the

capabilities that these software have to do real engineering work. From the analysis, a reasonable

first approximation stress distribution was found of the rotor blade.

References

[1] University of Liverpool, “Composite Materials and Helicopter Rotor Blades,” accessed December 13,

2016, http://classroom.materials.ac.uk/caseRoto.php.

[2] Langley Research Center, “2DN00: 2D NACA 0012 Airfoil Validation Case,” accessed December 13,

2016, https://turbmodels.larc.nasa.gov/naca0012_val.html.

[3] Performance Composites, “Mechanical Properties of Carbon Fibre Composite Materials,” accessed

December 13, 2016, http://www.performance

composites.com/carbonfibre/mechanicalproperties_2.asp

[4] Olson, L., Abrego, A., Barrows, D., and Burner, A., 2010, “Blade Deflection Measurements

of a Full-Scale UH-60A Rotor System,” Proceedings of the AHSAS, San Francisco, California,

January 20-22, 2010.

[5] Guruswamy, G., 2011, “CFD-based Computations of Flexible Helicopter Blades for Stability

Analysis,” NASA Advanced Supercomputing Division Ames Research Center, Moffett Field,

CA.

[6] Jiang, N., Ma, X., and Zhang, Z., 2005, “The Dynamic Characteristics Analysis of Rotor

Blade Based on ANSYS, ” The Research Institute of Simulation Technology of Nanjing.

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Appendix A: ANSYS Outputs

Figure A1: Deformations at 20 rad/s

Figure A2: Von Mises Stress at 20 rad/s

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Figure A3: Max Principal Stress at 20 rad/s

Figure A4: Max Shear Stress at 20 rad/s

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Figure A5: Deformations at 35 rad/s

Figure A6: Von Mises Stress at 35 rad/s

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Figure A7: Max Principal Stress at 35 rad/s

Figure A8: Max Shear Stress at 35 rad/s

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Figure A9: Deformations at 50 rad/s

Figure A10: Von Mises Stress at 50 rad/s

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Figure A11: Von Mises Stress at 50 rad/s

Figure A12: Von Mises Stress at 50 rad/s

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Figure A13: Max Principal Stress at 50 rad/s

Figure A14: Max Shear Stress at 50 rad/s

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Appendix B: Final Presentation